# NCERT Class 8 Mathematics Chapter 4 Quadrilaterals Solutions: In-Text and Exercise Questions Explained | SwaVid

This document provides real questions from the NCERT Class 8 Mathematics textbook "Ganita Prakash", Chapter 4, "Quadrilaterals", along with step-by-step...

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# Quadrilaterals

## Find the gaps before this chapter finds them for you.

## Related chapters

Chapter 4 · Class 8 Mathematics

This document provides real questions from the NCERT Class 8 Mathematics textbook "Ganita Prakash", Chapter 4, "Quadrilaterals", along with step-by-step solutions. The questions include both in-text activities and end-of-chapter exercises, transcribed as closely as possible to the original wording found in the official NCERT PDF (hegp104.pdf) and related educational resources.

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In-text Questions

Answer: The angles formed by the diagonals with the sides are 30° and 60°. The angles at the intersection of diagonals are 60° and 120° (assuming one angle is 120°).

The specific angles depend on the diagram provided in the textbook. This solution assumes a common scenario where one angle formed by the diagonals is 120 degrees.

Exercise Questions

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- Assume a rectangle ABCD with diagonals AC and BD intersecting at point O. All angles of a rectangle are 90 degrees.
- The diagonals of a rectangle are equal in length and bisect each other. Therefore, AO = BO = CO = DO.
- Consider triangle AOB. Since AO = BO, triangle AOB is an isosceles triangle. Similarly, triangles BOC, COD, and DOA are isosceles.
- If one angle, say ∠AOB, is given (e.g., 120° as suggested by a search result), then in triangle AOB, ∠OAB = ∠OBA = (180° - 120°) / 2 = 30°.
- Since ∠DAB = 90°, then ∠DAO = ∠DAB - ∠OAB = 90° - 30° = 60°.
- In triangle DOA, since AO = DO, ∠ADO = ∠DAO = 60°. Therefore, ∠DOA = 180° - (60° + 60°) = 60°.
- Using vertically opposite angles, ∠BOC = ∠DOA = 60° and ∠COD = ∠AOB = 120°.
- In triangle BOC, since BO = CO, ∠OBC = ∠OCB = (180° - 60°) / 2 = 60°.
- In triangle COD, since CO = DO, ∠OCD = ∠ODC = (180° - 120°) / 2 = 30°.
- Thus, the angles formed by the diagonals with the sides are 30° and 60°.
- NCERT Class 8 Mathematics textbook: Ganita Prakash : Chapter 4: Quadrilaterals

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- [NCERT Class 8 Mathematics textbook: Ganita Prakash](https://ncert.nic.in/textbook.php)