Extra Questions: Class 8 Maths Chapter 4 Quadrilaterals

Practice questions beyond the textbook exercises, testing deeper understanding of quadrilateral properties for Class 8 Maths Chapter 4: Quadrilaterals. These Class 8 Mathematics Chapter 4 important questions are handy for last-minute exam practice.

Last Updated: September 23, 2026

Extra Questions: Class 8 Maths Chapter 4 Quadrilaterals

1. 1 (Assertion-Reason). Assertion: Every square is a rhombus. Reason: A square has all four sides equal.
   Solution: Both true, and the reason correctly explains the assertion — a rhombus is defined as a parallelogram with all sides equal, which a square satisfies.
2. 2 (Numerical). In a parallelogram, one angle is 65°. Find all four angles.
   Solution: Opposite angles are equal and co-interior angles sum to 180°: 65°, 115°, 65°, 115°.
3. 3 (Synthesis). Can a trapezium have three right angles? Explain.
   Solution: No — three right angles would force the fourth to also be 90° (angle sum 360°), making it a rectangle, which has two pairs of parallel sides, not the trapezium’s single pair.
4. 4 (Applied). The diagonals of a rhombus are 6 cm and 8 cm. Find the length of each side.
   Solution: Diagonals bisect each other at right angles, giving half-diagonals 3 cm and 4 cm; by Pythagoras, side = √(3²+4²) = √25 = 5 cm.
5. 5 (Assertion-Reason). Assertion: A kite’s diagonals are always equal. Reason: A kite has two pairs of adjacent equal sides.
   Solution: Assertion is false (kite diagonals are generally unequal); reason is true but doesn’t support a false assertion — so the correct response is that the assertion is false.
6. 6 (Numerical). Three angles of a quadrilateral are 80°, 95°, and 100°. Find the fourth.
   Solution: 360−(80+95+100) = 85°.
7. 7 (Short Answer). Name the quadrilateral whose diagonals are equal, bisect each other, and are also perpendicular.
   Solution: Square.
8. 8 (Synthesis). If both pairs of opposite angles of a quadrilateral are equal, what can you conclude about its sides?
   Solution: It must be a parallelogram, so both pairs of opposite sides are equal and parallel.
9. 9 (Applied). ABCD is a parallelogram with ∠A=70°. Find ∠B, ∠C, ∠D.
   Solution: ∠B=110° (co-interior), ∠C=70° (opposite to A), ∠D=110° (opposite to B).
10. 10 (Assertion-Reason). Assertion: An isosceles trapezium’s base angles are equal. Reason: Its non-parallel sides (legs) are equal in length.
    Solution: Both true, and the reason correctly explains the assertion — equal legs in an isosceles trapezium produce equal base angles on each parallel side.

Frequently Asked Questions

How can you find a missing angle in a quadrilateral if the other three angles are known?
Since the sum of the interior angles of any quadrilateral is always 360 degrees, the missing angle can be found by adding the three known angles together and subtracting that sum from 360 degrees.

What property distinguishes a rhombus from a general parallelogram?
A rhombus is a special parallelogram in which all four sides are equal in length, and its diagonals bisect each other at right angles, properties a general parallelogram does not necessarily have.

Written by Satish

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