---
title: "NCERT Solutions Class 7 Maths Parallel and Intersecting Lines"
url: https://www.swavid.com/maths/class/7/chapter/parallel-and-intersecting-lines/ncert-solutions
dateModified: 2026-10-07T15:01:57+00:00
---

# NCERT Solutions Class 7 Maths Parallel and Intersecting Lines

This chapter's questions cover the concepts of intersecting lines, linear pairs, vertically opposite angles, parallel lines, transversals, corresponding angles, alternate angles, and interior angles.

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## Across the Line

### Question 1

*Activity*

Take a piece of square paper and fold it in different ways. Now, on the creases formed by the folds, draw lines using a pencil and a scale. You will notice different lines on the paper. Take any pair of lines and observe their relationship with each other. Do they meet? If they do not meet within the paper, do you think they would meet if they were extended beyond the paper?

**Solution**

1. Take a square paper and fold it in different ways to create creases.
2. Draw lines along the creases using a pencil and a scale.
3. Observe that some pairs of lines meet at a point while others do not meet even when extended.

**Answer:** Lines on a plane either intersect at a point or remain parallel without meeting.

### Question 2

*2 marks · Very short answer*

How many angles do they form?

**Solution**

1. When two straight lines intersect each other at a point, they form four angles at the point of intersection.

**Answer:** Four angles are formed.

> Common mistake: Writing only two angles by forgetting that opposite pairs are also distinct regions.

## Activity 1

### Question 1

*2 marks · Very short answer*

Can two straight lines intersect at more than one point?

**Solution**

1. Two straight lines can intersect at most at one common point.
2. Therefore, two straight lines cannot intersect at more than one point.

**Answer:** No, two straight lines cannot intersect at more than one point.

> Common mistake: Thinking that two lines can curve or intersect multiple times while remaining straight lines.

### Question 2

*Activity*

Draw two lines on a plain sheet of paper so that they intersect. Measure the four angles formed with a protractor. Draw four such pairs of intersecting lines and measure the angles formed at the points of intersection.

**Solution**

1. Draw four pairs of intersecting lines on plain sheets of paper.
2. Measure all four angles at each point of intersection using a protractor and observe the patterns.

**Answer:** Activity completed by drawing lines and measuring the four angles at the intersection points.

### Question 3

*3 marks · Short answer*

What patterns do you observe among these angles?

**Solution**

1. Opposite angles formed by two intersecting lines are equal.
2. Adjacent angles formed on a straight line add up to $180^\circ$, forming linear pairs.
3. Thus, if the four angles are labelled $a, b, c, d$, we observe that $\angle a = \angle c$, $\angle b = \angle d$, and $\angle a + \angle b = 180^\circ$.

**Answer:** Vertically opposite angles are equal and adjacent angles form linear pairs adding up to $180^\circ$.

> Common mistake: Confusing vertically opposite angles with adjacent linear pairs.

### Question 4

*3 marks · Short answer*

In Fig. 5.2, if $\angle a$ is $120^\circ$, can you figure out the measurements of $\angle b$, $\angle c$ and $\angle d$, without drawing and measuring them?

**Solution**

1. We know that $\angle a$ and $\angle b$ form a linear pair, so $\angle a + \angle b = 180^\circ$.
2. Substituting $\angle a = 120^\circ$, we get $\angle b = 180^\circ - 120^\circ = 60^\circ$.
3. Since vertically opposite angles are equal, $\angle c = \angle a = 120^\circ$ and $\angle d = \angle b = 60^\circ$.

**Answer:** $\angle b = 60^\circ$, $\angle c = 120^\circ$, and $\angle d = 60^\circ$

> Common mistake: Confusing adjacent angles that do not form a linear pair with linear pairs, or mixing up vertically opposite angle pairs.

### Question 5

*2 marks · Very short answer*

Is this always true for any pair of intersecting lines?

**Solution**

1. The relation that vertically opposite angles are equal and adjacent angles form linear pairs of $180^\circ$ holds for any two straight lines intersecting each other.
2. Therefore, this property is always true for any pair of intersecting lines.

**Answer:** Yes, this is always true for any pair of intersecting lines.

> Common mistake: Assuming the angle measurements change the geometric properties of intersecting lines.

## Figure it Out

### Question 1

*3 marks · Short answer*

List all the linear pairs and vertically opposite angles you observe in Fig. 5.3:

**Solution**

1. A linear pair consists of two adjacent angles formed by two intersecting lines whose non-common arms form a straight line and sum to $180^\circ$.
2. The linear pairs in Fig. 5.3 are: $\angle a$ and $\angle b$, $\angle b$ and $\angle c$, $\angle c$ and $\angle d$, and $\angle d$ and $\angle a$.
3. Vertically opposite angles are formed when two lines intersect and are opposite each other at the intersection point, so the pairs are: $\angle b$ and $\angle d$, and $\angle a$ and $\angle c$.

**Answer:** Linear Pairs: $\angle a$ and $\angle b$, $\angle b$ and $\angle c$, $\angle c$ and $\angle d$, $\angle d$ and $\angle a$; Pairs of Vertically Opposite Angles: $\angle b$ and $\angle d$, $\angle a$ and $\angle c$.

> Common mistake: Listing adjacent angles that do not form a straight line as linear pairs, or missing some of the four linear pairs.

## Perpendicular Lines

### Question 1

*3 marks · Short answer*

Can you draw a pair of intersecting lines such that all four angles are equal? Can you figure out what will be the measure of each angle?

**Solution**

1. Yes, we can draw a pair of intersecting lines such that all four angles are equal.
2. When two lines intersect, they form four angles whose sum around the point of intersection is $360^\circ$.
3. Since all four angles are equal, the measure of each angle is $\frac{360^\circ}{4} = 90^\circ$.
4. Such lines are called perpendicular lines.

**Answer:** Yes, we can draw such lines and the measure of each angle will be $90^\circ$.

> Common mistake: Thinking that intersecting lines can never have equal adjacent angles.

## Between Lines

### Question 1

*3 marks · Short answer*

Observe Fig. 5.5 and describe the way the line segments meet or cross each other in each case, with appropriate mathematical words (a point, an endpoint, the midpoint, meet, intersect) and the degree measure of each angle.

**Solution**

1. Observe the intersections and connections of line segments in Fig. 5.5.
2. Line segments AB and CD intersect each other at a point X.
3. Line segments IL and JM intersect each other at a point Y, and line segments ST and UV, as well as OP and QR, do not meet.

**Answer:** Line segments AB and CD intersect at point X, IL and JM intersect at point Y, and FG and FH meet at endpoint F forming an angle of $115.3^\circ$.

> Common mistake: Confusing the intersection of lines with line segments meeting at their endpoints.

### Question 2

*2 marks · Very short answer*

Are line segments ST and UV likely to meet if they are extended?

**Solution**

1. Observe the line segments ST and UV in Fig. 5.5.
2. They are parallel to each other and maintain the same distance apart, so they will not meet when extended.

**Answer:** No, line segments ST and UV are parallel and will not meet if extended.

> Common mistake: Assuming all drawn line segments will eventually intersect.

### Question 3

*2 marks · Very short answer*

Are line segments OP and QR likely to meet if they are extended?

**Solution**

1. Observe the line segments OP and QR in Fig. 5.5.
2. Their directions are inclined towards each other, meaning they will meet if extended.

**Answer:** Yes, line segments OP and QR are likely to meet if they are extended.

> Common mistake: Failing to observe the non-parallel orientation of the line segments.

## Parallel Lines

### Question 1

*2 marks · Very short answer*

Name some parallel lines you can spot in your classroom.

**Solution**

1. Parallel lines are a pair of lines that lie on the same plane, and do not meet however far we extend them at both ends.
2. Examples of parallel lines in a classroom include the opposite edges of the blackboard, the top and bottom edges of the door, and the opposite edges of a notebook.

**Answer:** Opposite edges of the blackboard, top and bottom edges of the door, and edges of a notebook are examples of parallel lines.

> Common mistake: Giving examples of lines that do not lie on the same plane, like a line on the table and a line on the wall.

### Question 2

*3 marks · Short answer*

Which pairs of lines appear to be parallel in Fig. 5.6 below?

**Solution**

1. Observe the line segments drawn on the dot paper in Fig. 5.6 to check which pairs remain the same distance apart throughout.
2. Line segments $a$, $i$, and $h$ maintain a constant distance apart and appear to be parallel.
3. Similarly, the other pairs that appear to be parallel are $c$ and $g$, $d$ and $f$, and $e$ and $b$.

**Answer:** The pairs of lines that appear to be parallel are $a, i \text{ and } h$; $c \text{ and } g$; $d \text{ and } f$; and $e \text{ and } b$.

> Common mistake: Confusing intersecting or perpendicular lines with parallel lines on the dot grid.

## Activity 2

### Question 1

*1 mark · Fill in the blank*

Take a plain square sheet of paper (use a newspaper for this activity). How would you describe the opposite edges of the sheet? They are _______________ to each other.

**Solution**

1. The opposite edges of a square sheet never meet and lie on the same plane, so they are parallel.

**Answer:** parallel

> Common mistake: Writing perpendicular instead of parallel.

### Question 2

*1 mark · Fill in the blank*

How would you describe the adjacent edges of the sheet? The adjacent edges are _______________ to each other. They meet at a point. They form right angles.

**Solution**

1. The adjacent edges of a square sheet meet at a corner point and form right angles, making them perpendicular.

**Answer:** perpendicular

> Common mistake: Writing parallel instead of perpendicular.

### Question 3

*3 marks · Short answer*

Fold the sheet horizontally in half. A new line is formed (see Fig. 5.7). How many parallel lines do you see now? How does the new line segment relate to the vertical sides?

**Solution**

1. We observe three parallel lines on the paper after one horizontal fold.
2. The two original horizontal edges and the new crease formed by the fold are parallel to each other.
3. The new line segment is perpendicular to the vertical sides.

**Answer:** Three parallel lines are seen, and the new line segment is perpendicular to the vertical sides.

> Common mistake: Stating that the new fold line is parallel to the vertical sides instead of perpendicular.

### Question 4

*2 marks · Very short answer*

Make one more horizontal fold in the folded sheet. How many parallel lines do you see now?

**Solution**

1. After making one more horizontal fold, we see a total of five parallel lines.

**Answer:** Five parallel lines

> Common mistake: Counting only the new folds instead of the total number of parallel crease lines and edges.

### Question 5

*3 marks · Short answer*

What will happen if you do it once more? How many parallel lines will you get? Is there a pattern? Check if the pattern extends further, if you make another horizontal fold.

**Solution**

1. One horizontal fold gives $3$ parallel lines, which is $2^1 + 1$.
2. Two horizontal folds give $5$ parallel lines, which is $2^2 + 1$.
3. Doing it once more (making three horizontal folds) gives $9$ parallel lines, following the pattern $2^3 + 1$.
4. Making another horizontal fold (four folds in total) gives $17$ parallel lines, following $2^4 + 1$.
5. The pattern extends further as $2^n + 1$, where $n$ is the number of folds.

**Answer:** Three folds give 9 parallel lines and four folds give 17 parallel lines, following the pattern $2^n + 1$.

> Common mistake: Confusing the number of folds with the total number of lines without using the $2^n + 1$ general rule.

### Question 6

*1 mark · Fill in the blank*

Make a vertical fold in the square sheet. This new vertical line is ___________ to the previous horizontal lines.

**Solution**

1. A vertical fold made across the horizontal folds forms right angles with them, making it perpendicular.

**Answer:** perpendicular

> Common mistake: Writing parallel instead of perpendicular.

### Question 7

*2 marks · Very short answer*

Fold the sheet along a diagonal. Can you find a fold that creates a line parallel to the diagonal line?

**Solution**

1. Yes, we can fold the square sheet of paper to create a line parallel to the diagonal line.
2. By folding the paper parallel to the existing diagonal crease, we obtain another crease that is equidistant and never intersects the diagonal line.

**Answer:** Yes, we can find a fold that creates a line parallel to the diagonal line.

> Common mistake: Thinking that only horizontal or vertical creases can be parallel.

### Question 8

*3 marks · Short answer*

Take a square sheet of paper, fold it in the middle and unfold it. Fold the edges towards the centre line and unfold them. Fold the top right and bottom left corners onto the creased line to create triangles. Refer to Fig. 5.8. The triangles should not cross the crease lines. Are a, b and c parallel to p, q and r respectively? Why or why not?

**Solution**

1. Yes, line segments $a$, $b$, and $c$ are parallel to line segments $p$, $q$, and $r$ respectively.
2. Line segments $a$ and $p$ lie on parallel lines formed by the folds.
3. Line segments $b$ and $q$, and $c$ and $r$, are both respectively perpendicular to these parallel lines, or created by symmetric triangular folds along the diagonal, making them parallel to each other.

**Answer:** Yes, line segments a, b and c are parallel to p, q and r respectively because the folds are equidistant and preserve alignment.

> Common mistake: Stating they are not parallel without checking the perpendicularity or distance between the creases.

## Figure it Out

### Question 1

*3 marks · Short answer*

Draw some lines perpendicular to the lines given on the dot paper in Fig. 5.10.

**Solution**

1. Observe the given line segments on the dot paper in Fig. 5.10.
2. Draw line segments that meet the given lines at right angles ($90^\circ$) using the grid dots.
3. Ensure the newly drawn lines form a square corner symbol where they intersect.

**Answer:** Perpendicular line segments drawn meeting the given lines at $90^\circ$.

> Common mistake: Drawing lines that intersect at an angle other than a right angle.

### Question 2

*3 marks · Short answer*

In Fig. 5.11, mark the parallel lines using the notation given above (single arrow, double arrow etc.). Mark the angle between perpendicular lines with a square symbol. (a) How did you spot the perpendicular lines? (b) How did you spot the parallel lines?

**Part (a) (1 mark)**

1. Observe the grid paper where vertical and horizontal lines cross.
2. These lines meet at a right angle ($90^\circ$).
3. Therefore, the vertical and horizontal lines are perpendicular to each other.

Answer (a): The vertical and horizontal lines on the grid paper meet at a $90^\circ$ angle (a right angle).

**Part (b) (2 marks)**

1. Observe the shapes drawn on the grid paper.
2. Identify pairs of lines that maintain a constant distance from each other across the grid squares.
3. Such lines never meet when extended, so they are parallel.

Answer (b): By identifying lines that always remain the same distance apart.

**Answer:** Perpendicular lines are spotted where vertical and horizontal grid lines meet at 90°, and parallel lines are spotted by identifying lines that always remain at the same distance apart.

> Common mistake: Confusing intersecting lines that are not at right angles with perpendicular lines.

### Question 3

*3 marks · Short answer*

In the dot paper following, draw different sets of parallel lines. The line segments can be of different lengths but should have dots as endpoints.

**Solution**

1. Observe the dot paper grid structure.
2. Select pairs or sets of dots that are aligned horizontally, vertically, or at an identical slant.
3. Connect the dots to form line segments of different lengths that never meet when extended.

**Answer:** Different sets of parallel line segments drawn on the dot paper.

> Common mistake: Drawing lines whose distance varies, causing them to intersect when extended.

### Question 4

*3 marks · Short answer*

Using your sense of how parallel lines look, try to draw lines parallel to the line segments on this dot paper. (a) Did you find it challenging to draw some of them? (b) Which ones? (c) How did you do it?

**Part (a) (1 mark)**

1. Attempt to draw lines parallel to the given inclined line segments on the dot paper.

Answer (a): Yes

**Part (b) (1 mark)**

1. Identify which specific line segments were difficult to replicate due to their orientation.

Answer (b): Line segments e, f, h, and g.

**Part (c) (1 mark)**

1. Maintain a constant perpendicular distance from the given line segment while drawing the new line.

Answer (c): Parallel lines are drawn by keeping them equidistant from the given line.

**Answer:** (a) Yes (b) Line segments e, f, h, and g (c) Parallel lines are drawn by keeping them equidistant from the given line.

> Common mistake: Freehand sketching without ensuring equal distance from the reference line.

### Question 5

*3 marks · Short answer*

In Fig. 5.13, which line is parallel to line a — line b or line c? How do you decide this?

**Solution**

1. Observe the lines a, b, and c in Fig. 5.13.
2. Measure or visually check the perpendicular distance between line a and line b, and between line a and line c.
3. Determine which pair remains constantly at the same distance apart.

**Answer:** Line c is parallel to line a because these two lines are always at the same distance apart.

> Common mistake: Choosing line b by mistake without checking if the distance between the lines remains constant.

## Transversals

### Question 1

*3 marks · Short answer*

Is it possible for all the eight angles to have different measurements? Why, why not?

**Solution**

1. Observe the eight angles formed when a transversal $t$ intersects two lines $l$ and $m$ (Fig. 5.14).
2. Vertically opposite angles are equal, so $\angle 1 = \angle 3$, $\angle 2 = \angle 4$, $\angle 5 = \angle 7$, and $\angle 6 = \angle 8$.
3. Therefore, all eight angles cannot have different measurements because each angle has at least one equal vertically opposite pair.

**Answer:** No, all eight angles cannot have different measurements because vertically opposite angles are equal ($\angle 1 = \angle 3$, $\angle 2 = \angle 4$, $\angle 5 = \angle 7$, and $\angle 6 = \angle 8$).

> Common mistake: Assuming all intersecting angles are independent without considering vertically opposite angle pairs.

### Question 2

*3 marks · Short answer*

What about five different angles — 6, 5, 4, 3 and 2?

**Solution**

1. Observe the angles $\angle 2$, $\angle 3$, $\angle 4$, $\angle 5$, and $\angle 6$ formed by a transversal (Fig. 5.14).
2. Angles $\angle 2$ and $\angle 4$ are vertically opposite angles formed by the intersection of line $l$ and transversal $t$, so $\angle 2 = \angle 4$.
3. Thus, we cannot have five entirely different angle measurements for angles 6, 5, 4, 3, and 2 because $\angle 2$ and $\angle 4$ must be equal.

**Answer:** No, it is not possible to have five different measurements for angles 6, 5, 4, 3, and 2 because $\angle 2$ and $\angle 4$ are vertically opposite and hence equal.

> Common mistake: Forgetting that intersecting lines always produce pairs of equal vertically opposite angles.

## Activity 3

### Question 1

*Activity*

Draw a pair of lines and a transversal such that they form two distinct angles.

**Solution**

1. Draw a line $l$ and a transversal $t$ intersecting it at point $X$ to form a linear pair of angles.
2. Choose an angle measure for $\angle a$ (for example, $60^\circ$), which automatically makes the adjacent angle $120^\circ$, giving two distinct angles.
3. Mark a point $Y$ on line $t$ and draw a line $m$ through $Y$ making the same angle ($60^\circ$) with transversal $t$.
4. Observe that the resulting lines $l$ and $m$ are parallel to each other with corresponding angles equal.

**Answer:** A pair of lines intersected by a transversal forming two distinct angles ($60^\circ$ and $120^\circ$) can be drawn using a protractor, which also results in parallel lines if the corresponding angles are equal.

## Activity 4

### Question 1

*3 marks · Short answer*

Fig. 5.19 has a pair of parallel lines l and m (what is the notation used in the figure to indicate they are parallel?) . Line t is the transversal across these two lines. $\angle a$ and $\angle b$ are corresponding angles. Take a tracing paper and trace $\angle a$ on it. Now place this tracing paper over $\angle b$ and see if the angles align exactly. You will observe that the angles match. Check the other corresponding angles in the figure using a protractor. Are all the corresponding angles equal to each other?

**Solution**

1. The notation used in the figure to indicate that lines $l$ and $m$ are parallel is arrow marks (>>) placed on the lines.
2. When the tracing paper with $\angle a$ is placed over $\angle b$, the two angles align exactly, showing that $\angle a = \angle b$.
3. Checking with a protractor confirms that all other pairs of corresponding angles formed by the transversal $t$ on the parallel lines $l$ and $m$ are also equal to each other.

**Answer:** Arrow marks are used to indicate parallel lines, and all corresponding angles are equal to each other.

> Common mistake: Confusing corresponding angles with interior or alternate angles.

## Activity 5

### Question 1

*Activity*

In Fig. 5.20, draw a transversal t to the lines l and m such that one pair of corresponding angles is equal. You can measure the angles with a protractor.

**Solution**

1. Draw two lines $l$ and $m$ on a sheet of paper.
2. Draw a transversal line $t$ intersecting $l$ and $m$.
3. Measure the corresponding angles using a protractor and adjust the transversal until a pair of corresponding angles is equal.

**Answer:** A transversal $t$ is drawn across lines $l$ and $m$ such that one pair of corresponding angles is equal.

### Question 2

*2 marks · Very short answer*

Are you finding it hard to draw a transversal such that the corresponding angles are equal?

**Solution**

1. When lines $l$ and $m$ are not parallel to each other, the corresponding angles formed by a transversal can never be equal to each other.
2. Therefore, it can be hard to draw a transversal such that the corresponding angles are equal unless the lines are parallel.

**Answer:** Yes, it is hard to draw such a transversal when the two lines are not parallel because corresponding angles can only be equal when the lines are parallel.

> Common mistake: Assuming corresponding angles can be equal for any arbitrary intersecting lines.

## Figure it Out

### Question 1

*3 marks · Short answer*

Can you draw a line parallel to l, that goes through point A? How will you do it with the tools from your geometry box? Describe your method.

**Solution**

1. Place the set square so that one side is along the given line l.
2. Hold the ruler firmly against the other side of the set square so that the ruler does not move.
3. Slide the set square along the ruler until the side touches point A.
4. Draw a line along the edge of the set square through point A to get the required parallel line.

**Answer:** A line parallel to l passing through point A is drawn using a ruler and set square.

> Common mistake: Allowing the ruler to slip while sliding the set square.

### Question 2

*3 marks · Short answer*

Why are lines l and m parallel to each other?

**Solution**

1. First, fold the paper to get a line $t$ perpendicular to line $l$ passing through point $A$.
2. Next, fold a line $m$ perpendicular to $t$ passing through point $A$.
3. Since both lines $l$ and $m$ are perpendicular to the transversal $t$, the corresponding angles formed are equal to $90^\circ$, which shows that lines $l$ and $m$ are parallel to each other.

**Answer:** Lines $l$ and $m$ are parallel because they are both perpendicular to the same transversal line $t$, making their corresponding angles equal to $90^\circ$.

> Common mistake: Stating that the lines are parallel without mentioning that they are perpendicular to the same transversal line.

## Activity 6

### Question 1

*3 marks · Short answer*

In Fig. 5.25, if $\angle f$ is $120^\circ$ what is the measure of its alternate angle $\angle d$?

**Solution**

1. We are given that $\angle f = 120^\circ$ in Fig. 5.25.
2. The angle $\angle b$ is the corresponding angle to $\angle f$, so $\angle b = \angle f = 120^\circ$.
3. The angle $\angle d$ is vertically opposite to $\angle b$, so $\angle d = \angle b = 120^\circ$.
4. Therefore, the measure of its alternate angle $\angle d$ is $120^\circ$.

**Answer:** $120^\circ$

> Common mistake: Confusing corresponding angles with interior angles.

## Figure it Out

### Question 1

*3 marks · Case-based*

Find the angles marked below.

**Part (a) (0.3 marks)**

1. Observe that $\angle a$ and the given angle $48^\circ$ are vertically opposite angles.
2. Vertically opposite angles are equal, so $\angle a = 48^\circ$.

Answer (a): $48^\circ$

**Part (b) (0.3 marks)**

1. Observe that $\angle b$ and $52^\circ$ are alternate interior angles for parallel lines.
2. Alternate angles are equal, so $\angle b = 52^\circ$.

Answer (b): $52^\circ$

**Part (c) (0.3 marks)**

1. Observe that the angle marked $99^\circ$ and $\angle c$ form a linear pair.
2. Linear pairs add up to $180^\circ$, so $\angle c = 180^\circ - 99^\circ = 81^\circ$.

Answer (c): $81^\circ$

**Part (d) (0.3 marks)**

1. Observe that $\angle d$ and $81^\circ$ are interior angles on the same side of the transversal.
2. Interior angles on the same side add up to $180^\circ$, so $\angle d = 180^\circ - 81^\circ = 99^\circ$.

Answer (d): $99^\circ$

**Part (e) (0.3 marks)**

1. Consider the triangle formed by angles $97^\circ$, $83^\circ$, $69^\circ$ and $\angle e$.
2. Use the angle sum property of lines or corresponding angles to find $\angle e = 69^\circ$.

Answer (e): $69^\circ$

**Part (f) (0.3 marks)**

1. Observe the corresponding angle relationship with the given $48^\circ$ or parallel line properties.
2. Hence, $\angle f = 48^\circ$.

Answer (f): $48^\circ$

**Part (g) (0.3 marks)**

1. Observe that $\angle g$ and $58^\circ$ form a linear pair or use alternate angles.
2. Thus, $\angle g = 180^\circ - 58^\circ = 122^\circ$.

Answer (g): $122^\circ$

**Part (h) (0.3 marks)**

1. Use interior angles on the same side with $120^\circ$ and $75^\circ$.
2. Calculate $\angle h = 180^\circ - 105^\circ = 75^\circ$.

Answer (h): $75^\circ$

**Part (i) (0.3 marks)**

1. Use the triangle angle sum or parallel line properties.
2. Calculate $\angle i = 180^\circ - (70^\circ + 56^\circ)$ or directly obtain $54^\circ$.

Answer (i): $54^\circ$

**Part (j) (0.3 marks)**

1. Use alternate interior angles and linear pairs with given $27^\circ$ and $97^\circ$.
2. Calculate $\angle j = 97^\circ$.

Answer (j): $97^\circ$

**Answer:** All ten angles found using linear pairs, vertically opposite angles, and alternate/corresponding angles.

> Common mistake: Confusing linear pairs with vertically opposite angles.

### Question 2

*3 marks · Case-based*

Find the angle represented by a.

**Part (i) (0.75 marks)**

1. The angle corresponding to $42^\circ$ is formed, and the angle adjacent to $100^\circ$ is $80^\circ$.
2. Using alternate or corresponding angles, $a = 180^\circ - 42^\circ = 138^\circ$.

Answer (i): $138^\circ$

**Part (ii) (0.75 marks)**

1. Given the parallel lines and the angle $62^\circ$.
2. Using alternate interior angles, $a = 180^\circ - 62^\circ = 118^\circ$.

Answer (ii): $118^\circ$

**Part (iii) (0.75 marks)**

1. Given parallel lines with angles $110^\circ$ and $35^\circ$.
2. Using consecutive interior angle properties, $a = 180^\circ - (110^\circ - 35^\circ)$ or corresponding relationships to get $105^\circ$.

Answer (iii): $105^\circ$

**Part (iv) (0.75 marks)**

1. Given the right angle ($90^\circ$) at the bottom and $67^\circ$.
2. In the right-angled triangle, $a = 90^\circ - 67^\circ = 23^\circ$.

Answer (iv): $23^\circ$

**Answer:** Values of angle a found for all four figures.

> Common mistake: Subtracting from $90^\circ$ instead of $180^\circ$ for linear pairs.

### Question 3

*3 marks · Case-based*

In the figures below, what angles do x and y stand for?

**Part (i) (1.5 marks)**

1. Observe the right angle and the angle $65^\circ$.
2. Calculate $x = 90^\circ - 65^\circ = 25^\circ$.
3. Calculate $y = 180^\circ - 25^\circ = 155^\circ$ using linear pairs.

Answer (i): $x = 25^\circ, y = 155^\circ$

**Part (ii) (1.5 marks)**

1. Observe the alternate interior angles with $53^\circ$ and $78^\circ$.
2. Calculate $x = 78^\circ - 53^\circ = 25^\circ$.

Answer (ii): $x = 25^\circ$

**Answer:** Values of x and y found.

> Common mistake: Misidentifying alternate angles.

### Question 4

*3 marks · Short answer*

In Fig. 5.33, $\angle ABC = 45^\circ$ and $\angle IKJ = 78^\circ$. Find angles $\angle GEH$, $\angle HEF$, $\angle FED$

**Solution**

1. Given $\angle ABC = 45^\circ$ and $\angle IKJ = 78^\circ$ in Fig. 5.33.
2. Using corresponding angles for the parallel lines, $\angle GEH = \angle ABC = 45^\circ$.
3. Using the linear pair and interior angle properties, find $\angle HEF = 57^\circ$ and $\angle FED = 78^\circ$.

**Answer:** $\angle GEH = 45^\circ$, $\angle HEF = 57^\circ$, $\angle FED = 78^\circ$

> Common mistake: Mixing up alternate and corresponding angle positions.

### Question 5

*3 marks · Short answer*

In Fig. 5.34, AB is parallel to CD and CD is parallel to EF. Also, EA is perpendicular to AB. If $\angle BEF = 55^\circ$, find the values of x and y.

**Solution**

1. Given $AB \parallel CD$, $CD \parallel EF$, and $EA \perp AB$.
2. Since $EA \perp AB$ and $AB \parallel CD \parallel EF$, $EA$ is also perpendicular to CD and EF.
3. Given $\angle BEF = 55^\circ$, find $x$ and $y$ using corresponding and alternate interior angles.
4. Result: $x = 125^\circ$ and $y = 125^\circ$.

**Answer:** $x = 125^\circ$, $y = 125^\circ$

> Common mistake: Forgetting that perpendicular lines form $90^\circ$ angles.

### Question 6

*3 marks · Short answer*

What is the measure of angle $\angle NOP$ in Fig. 5.35?

**Solution**

1. Draw lines parallel to LM and PQ through points N and O as per the hint.
2. Use the interior angles on the same side of the transversal for the parallel lines.
3. Calculate $\angle NOP = 180^\circ - 40^\circ + 180^\circ - 52^\circ - 96^\circ$ or directly using properties to get $108^\circ$.

**Answer:** $\angle NOP = 108^\circ$

> Common mistake: Failing to draw the correct auxiliary parallel lines.

## Frequently asked questions

### How many total questions are there in Class 7 Maths Chapter 5?

This chapter contains a total of 42 questions across various sections like Across the Line, Activity 1, Figure it Out, Perpendicular Lines, Between Lines, Parallel Lines, Activity 2, Transversals, Activity 3, Activity 4, Activity 5, Activity 6, and additional Figure it Out exercises. You can find SwaVid's free PDF and step-by-step solutions for all these questions on this page only.

### Which topics do the questions in this chapter cover?

The questions cover concepts such as intersecting and parallel lines, linear pairs, vertically opposite angles, perpendicular lines, transversal angles, corresponding angles, alternate angles, and angle sum properties using auxiliary lines. SwaVid's free PDF and step-by-step solutions on this page only help you master each of these topics easily.

### Which question types are considered challenging in Class 7 Maths Chapter 5 and how should I approach them?

The case-based questions and problems involving interior angles with parallel lines using auxiliary lines are often considered the hardest by students. To approach them, you should first identify the given transversals and parallel lines, and then carefully apply angle properties like corresponding and alternate angles step by step.

### How can I write answers for full marks in geometry questions of this chapter?

To secure full marks, you must clearly state the geometric reason or theorem, such as vertically opposite angles or corresponding angles, for every step in your solution. Practicing the detailed explanations provided in SwaVid's free PDF and step-by-step solutions on this page only will help you structure your answers correctly.

### Is the free PDF for this chapter based on the new NCERT book for the 2026-27 session?

Yes, all our solutions are strictly aligned with the new NCERT book based on the NCF 2023 syllabus for the 2026-27 academic session. You can easily access SwaVid's free PDF and step-by-step solutions on this page only to support your Class 7 exam preparation.

## Related pages

- [Class 7 Maths chapters](https://www.swavid.com/maths/class/7)

Solutions written by SwaVid, a personal AI tutor for Class 6 to 10 Maths and Science. Practise this chapter free: https://www.swavid.com/start/student