Quadrilaterals — Class 8 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 8 Mathematics chapter "Quadrilaterals" — 7 important questions with detailed answers for CBSE board exam preparation.

TL;DR: Free step-by-step NCERT solutions for Class 8 Mathematics chapter "Quadrilaterals" — 7 important questions with detailed answers for CBSE board exam p…

By Syllab.in · Updated Jun 14, 2026

Key Questions Covered:

Find the fourth angle of a quadrilateral if three angles are 70°, 85°, and 95°.
Identify the quadrilateral with all sides equal and all angles equal.
In a parallelogram ABCD, angle A = 60°. Find angles B, C, and D.
What is the sum of an interior angle and an exterior angle of a quadrilateral?
Classify the quadrilateral with one pair of parallel sides.
In rectangle PQRS, diagonals PR and QS intersect at O. If PO = 5 cm, find QS.
+ 1 more questions in the full chapter

Solutions Summary:

Question	Status
Find the fourth angle of a quadrilateral if three angles …	✓ Solved
Identify the quadrilateral with all sides equal and all a…	✓ Solved
In a parallelogram ABCD, angle A = 60°. Find angles B, C,…	✓ Solved
What is the sum of an interior angle and an exterior angl…	✓ Solved
Classify the quadrilateral with one pair of parallel sides.	✓ Solved
In rectangle PQRS, diagonals PR and QS intersect at O. If…	✓ Solved

Showing 6 of 7 questions

Q1: Find the fourth angle of a quadrilateral if three angles are 70°, 85°, and 95°.

We use the angle sum property of quadrilaterals. Step 1: Recall the angle sum property The sum of all interior angles of a quadrilateral = 360° Step 2: Let the fourth angle be x 70° + 85° + 95° + x = 360° Step 3: Add the three known angles 70 + 85 + 95 = 250 250 + x = 360° Step 4: Solve for x x = 360° - 250° x = 110° Step 5: Verify 70 + 85 + 95 + 110 = 360 ✓ Answer: The fourth angle is 110°

Q2: Identify the quadrilateral with all sides equal and all angles equal.

We need to identify which quadrilateral has these properties. Step 1: Analyze the property "all sides equal" Quadrilaterals with all sides equal: rhombus, square Step 2: Analyze the property "all angles equal" If all angles of a quadrilateral are equal: Each angle = 360°/4 = 90° Quadrilaterals with all angles = 90°: rectangle, square Step 3: Find the quadrilateral with both properties Rhombus: all sides equal, opposite angles equal (but not all angles equal) Square: all si...

Q3: In a parallelogram ABCD, angle A = 60°. Find angles B, C, and D.

We use the properties of angles in a parallelogram. Step 1: Recall properties of a parallelogram - Opposite angles are equal - Adjacent angles are supplementary (sum = 180°) Step 2: Find angle B Angles A and B are adjacent in the parallelogram A + B = 180° 60° + B = 180° B = 120° Step 3: Find angle C Angles A and C are opposite in the parallelogram C = A C = 60° Step 4: Find angle D Angles B and D are opposite in the parallelogram D = B D = 120° Alternatively, angles A and D are adjacent: A...

Q4: What is the sum of an interior angle and an exterior angle of a quadrilateral?

We need to find the relationship between an interior angle and its adjacent exterior angle. Step 1: Define exterior angle An exterior angle is formed by extending one side of the quadrilateral. The exterior angle and its adjacent interior angle are supplementary. Step 2: At any vertex of a quadrilateral Interior angle + Exterior angle = 180° (They form a linear pair) Step 3: Example If an interior angle is 80°, the exterior angle at that vertex is: 180° - 80° = 100° Sum = 80° + 100° = 180° S...

Q5: Classify the quadrilateral with one pair of parallel sides.

We need to identify the quadrilateral based on its side properties. Step 1: Recall quadrilateral types - Parallelogram: both pairs of opposite sides parallel - Trapezium (or Trapezoid): exactly one pair of parallel sides - Rhombus: all sides equal, opposite sides parallel - Rectangle: all angles 90°, opposite sides parallel - Square: all sides equal, all angles 90°, opposite sides parallel - Kite: two pairs of consecutive sides equal, but no parallel sides Step 2: Identify by "one pair of...

Q6: In rectangle PQRS, diagonals PR and QS intersect at O. If PO = 5 cm, find QS.

We use the property of diagonals in a rectangle. Step 1: Recall properties of rectangle diagonals - Diagonals of a rectangle are equal in length - Diagonals bisect each other - Each diagonal divides the rectangle into two congruent triangles Step 2: Since diagonals bisect each other O is the midpoint of both diagonals PR and QS Therefore: PO = OR and QO = OS Step 3: Given information PO = 5 cm Step 4: Find PR (the full diagonal) Since O is the midpoint of PR: PR = 2 × PO = 2 × 5 = 10 cm Ste...

Showing 6 of 7 questions. Visit the full page for complete solutions.