How many practice questions are available for Quadrilaterals?

SparkEd Math offers 60+ practice questions for Quadrilaterals across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Quadrilaterals content free on SparkEd Math?

Yes! All Quadrilaterals content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Quadrilaterals differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Quadrilaterals problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Quadrilaterals content aligned with the Olympiad syllabus?

Yes, all Quadrilaterals questions and lessons on SparkEd Math are fully aligned with the Mathematical Olympiad Preparation (Olympiad) syllabus for Class 8. The content follows the official curriculum structure and exam pattern.

Quadrilaterals — Class 8 Olympiad (2025-26)

About Quadrilaterals — Class 8 Olympiad

Explore properties of parallelograms, rhombuses, rectangles, and squares; solve angle and area problems. This topic is part of the Olympiad Class 8 mathematics syllabus (chapter: Module 10). On this page you can practice 59 questions across three difficulty levels — 19 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Quadrilaterals — solved examples for Class 8 Olympiad

Example 1easy

In a quadrilateral ABCD, the measures of the interior angles are ∠A = 2x, ∠B = 3x, ∠C = 4x, and ∠D = 3x. What is the measure of the smallest exterior angle of the quadrilateral?

A)30°
B)60°
C)90°
D)120°

Step-by-step solution

The sum of the interior angles of a quadrilateral is 360°. So, 2x + 3x + 4x + 3x = 360°.
This simplifies to 12x = 360°, which means x = 30°.
The interior angles are: ∠A = 2(30°) = 60°, ∠B = 3(30°) = 90°, ∠C = 4(30°) = 120°, ∠D = 3(30°) = 90°.
The corresponding exterior angles are: 180°-60°=120°, 180°-90°=90°, 180°-120°=60°, 180°-90°=90°. The smallest exterior angle is 60°.

Answer: 60°

Example 2medium

In a quadrilateral ABCD, ∠A = 110° and ∠B = 90°. The angle bisectors of ∠C and ∠D meet at point P. Find the measure of ∠CPD.

A)80°
B)90°
C)100°
D)110°

Step-by-step solution

The sum of interior angles of a quadrilateral ABCD is 360°. So, ∠A + ∠B + ∠C + ∠D = 360°.
Given ∠A = 110° and ∠B = 90°, we have 110° + 90° + ∠C + ∠D = 360°, which simplifies to 200° + ∠C + ∠D = 360°. Thus, ∠C + ∠D = 160°.
In triangle CPD, CP bisects ∠C and DP bisects ∠D. So, ∠PCD = ∠C/2 and ∠PDC = ∠D/2.
The sum of angles in ΔCPD is 180°. Therefore, ∠CPD + ∠PCD + ∠PDC = 180°. Substituting the bisected angles: ∠CPD + (∠C/2) + (∠D/2) = 180°.
This can be written as ∠CPD + (∠C + ∠D)/2 = 180°. Substitute ∠C + ∠D = 160°: ∠CPD + 160°/2 = 180°. ∠CPD + 80° = 180°. Hence, ∠CPD = 100°.

Answer: 100°

Example 3hard

In a convex quadrilateral ABCD, the angle bisectors of ∠A and ∠B meet at point P. The angle bisectors of ∠C and ∠D meet at point Q. If ∠APB = 100°, find the measure of ∠CQD.

A)70°
B)90°
C)100°
D)80°

Step-by-step solution

In ΔAPB, the sum of angles is 180°. So, ∠PAB + ∠PBA + ∠APB = 180°.
Given ∠APB = 100°, we have ∠PAB + ∠PBA = 180° - 100° = 80°. Since AP and BP are angle bisectors, (∠A/2) + (∠B/2) = 80°, which means ∠A + ∠B = 160°.
In quadrilateral ABCD, the sum of interior angles is 360°. So, ∠A + ∠B + ∠C + ∠D = 360°. Substituting ∠A + ∠B = 160°, we get 160° + ∠C + ∠D = 360°, which implies ∠C + ∠D = 200°.
In ΔCQD, the sum of angles is 180°. So, ∠QCD + ∠QDC + ∠CQD = 180°. Since CQ and DQ are angle bisectors, (∠C/2) + (∠D/2) + ∠CQD = 180°. This simplifies to (∠C + ∠D)/2 + ∠CQD = 180°. Substituting ∠C + ∠D = 200°, we get 200°/2 + ∠CQD = 180°, so 100° + ∠CQD = 180°. Therefore, ∠CQD = 80°.

Answer: 80°

Practice questions on Quadrilaterals

Q1.easy
Diagonals AC and BD of a parallelogram ABCD intersect at point O. If AO = (x+1) cm, OC = (2x-3) cm, BO = 10 cm, and OD = 10 cm, what is the value of x?
1. A)2
2. B)4
3. C)5
4. D)7
Show answer
Answer: 4
Hint: Recall the fundamental property of diagonals in a parallelogram regarding their intersection point.
Q2.easy
The perimeter of a rhombus is 52 cm. If one of its diagonals is 10 cm, what is the length of the other diagonal?
1. A)24 cm
2. B)13 cm
3. C)10 cm
4. D)12 cm
Show answer
Answer: 24 cm
Hint: A rhombus has four equal sides. Its diagonals bisect each other at right angles, forming four right-angled triangles.
Q3.easy
Three vertices of a square ABCD are A(1,2), B(5,2), and C(5,6). Find the coordinates of vertex D.
1. A)(1,5)
2. B)(2,6)
3. C)(1,6)
4. D)(6,1)
Show answer
Answer: (1,6)
Hint: Visualize the coordinates on a grid. In a square, opposite sides are parallel and equal, and adjacent sides are perpendicular.
Q4.medium
In parallelogram ABCD, the measure of angle A is (3x + 20)° and the measure of angle B is (2x + 10)°. Find the measure of angle D.
1. A)70°
2. B)80°
3. C)100°
4. D)110°
Show answer
Answer: 70°
Hint: Recall that consecutive angles in a parallelogram are supplementary. Use this to find the value of 'x' and subsequently the required angle.
Q5.medium
The diagonals of a rhombus are 30 cm and 16 cm. Find the perimeter of the rhombus.
1. A)52 cm
2. B)60 cm
3. C)68 cm
4. D)72 cm
Show answer
Answer: 68 cm
Hint: Remember that the diagonals of a rhombus bisect each other at right angles. This creates four congruent right-angled triangles.
Q6.medium
A rectangle has a diagonal of length 15 cm and its area is 108 cm². What is the perimeter of the rectangle?
1. A)36 cm
2. B)42 cm
3. C)48 cm
4. D)54 cm
Show answer
Answer: 42 cm
Hint: Let the length and width be 'l' and 'w'. Use the Pythagorean theorem for the diagonal and the area formula to form a system of equations.
Q7.hard
ABCD is a parallelogram. The angle bisector of ∠A meets DC at E. If ∠AEB = 80°, find ∠ADC.
1. A)10°
2. B)20°
3. C)30°
4. D)40°
Show answer
Answer: 20°
Hint: Use properties of parallel lines (alternate interior angles), angle bisectors, and angle sum in triangles and parallelograms.
Q8.hard
A rhombus PQRS has diagonals PR and QS intersecting at O. If the perimeter of the rhombus is 60 cm and the length of diagonal PR is 24 cm, find the area of the rhombus.
1. A)108 cm²
2. B)180 cm²
3. C)216 cm²
4. D)240 cm²
Show answer
Answer: 216 cm²
Hint: Use the perimeter to find the side length. Then, apply the Pythagorean theorem in one of the right-angled triangles formed by the diagonals.
Q9.hard
In a rectangle ABCD, the diagonals intersect at O. If ∠BOC = 124°, find ∠OAD.
1. A)62°
2. B)56°
3. C)31°
4. D)28°
Show answer
Answer: 62°
Hint: Recall that diagonals of a rectangle are equal and bisect each other, forming isosceles triangles.

These are 9 of the 59 questions available for Quadrilaterals. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.