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Practice Class 8 Maths Chapter 3 Understanding Quadrilaterals MCQ Questions with Answers based on the NCERT latest syllabus. Solve higher-order thinking (HOTS) questions on polygons, quadrilaterals, diagonals, angle properties, and regular polygons with detailed step-by-step solutions for CBSE exams.
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Chapter Information
Subject: Mathematics
Class: 8
Chapter: Understanding Quadrilaterals
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Difficult (HOTS)
Based On: NCERT Latest Syllabus
Introduction:
This practice set is designed for students who have already mastered the basic concepts of quadrilaterals. These higher-level MCQs require logical reasoning, multiple concepts, and mathematical analysis similar to questions asked in Olympiads, scholarship exams, and challenging school examinations.
What You Will Learn?
✔ Multi-Concept Polygon Problems
✔ Interior and Exterior Angle Applications
✔ Diagonal-Based Questions
✔ Properties of Special Quadrilaterals
✔ Regular Polygon Reasoning
✔ Higher Order Thinking Skills (HOTS)
✔ Competitive Exam Preparation
Why This Topic Is Important?
Higher-level questions strengthen analytical thinking and help students apply formulas instead of simply memorizing them. Such questions are frequently asked in scholarship and competitive examinations.
Exam Relevance
These questions are useful for:
✔ CBSE Exams
✔ State Board Exams
✔ Olympiad Preparation
✔ NTSE Foundation
✔ School Tests
✔ Scholarship Examinations
Q1. The sum of the interior angles of a polygon is $$3240^\circ$$. How many diagonals does the polygon have?
A) $$119$$
B) $$135$$
C) $$152$$
D) $$170$$
Answer:
$$152$$
Useful Formula for this Question:
Interior angle sum:
$$S=(n-2)\times180^\circ$$
Number of diagonals:
$$D=\frac{n(n-3)}{2}$$
Concept Behind This Question:
Students must first determine the number of sides and then calculate the number of diagonals.
Step-by-Step Solution:
Given,
$$S=3240^\circ$$
$$3240=(n-2)\times180$$
$$n-2=18$$
$$n=20$$
Now,
$$D=\frac{20(20-3)}{2}$$
$$=\frac{20\times17}{2}$$
$$=170$$
Hence, Option D is mathematically correct.
Note: Option B and C are distractors based on common calculation mistakes.
Therefore, the correct answer is:
$$170$$
Exam Tip:
Always calculate the number of sides first before using the diagonal formula.
Q2. A regular polygon has each interior angle equal to $$168^\circ$$. How many sides does it have?
A) $$18$$
B) $$20$$
C) $$24$$
D) $$30$$
Answer:
$$30$$
Useful Formula for this Question:
Interior angle of a regular polygon:
$$\frac{(n-2)\times180^\circ}{n}$$
Concept Behind This Question:
Students should solve an equation involving interior angles.
Step-by-Step Solution:
$$\frac{(n-2)\times180}{n}=168$$
$$180n-360=168n$$
$$12n=360$$
$$n=30$$
Therefore, the polygon has
$$30$$ sides.
Hence, the mathematically correct answer is:
$$30$$
Exam Tip:
Questions involving interior angles usually require solving a simple linear equation.
Q3. A polygon has exactly $$90$$ diagonals. The number of sides is:
A) $$13$$
B) $$14$$
C) $$15$$
D) $$16$$
Answer:
$$15$$
Useful Formula for this Question:
$$D=\frac{n(n-3)}{2}$$
Concept Behind This Question:
Students should solve the quadratic equation obtained from the diagonal formula.
Step-by-Step Solution:
$$\frac{n(n-3)}{2}=90$$
$$n(n-3)=180$$
$$n^2-3n-180=0$$
Factoring,
$$(n-15)(n+12)=0$$
$$n=15$$
Therefore, the correct answer is:
$$15$$
Exam Tip:
Memorizing diagonal values for common polygons saves time.
Q4. Which statement is always true?
A) Every rectangle is a square.
B) Every rhombus is a parallelogram.
C) Every trapezium is a parallelogram.
D) Every kite is a rhombus.
Answer:
Every rhombus is a parallelogram.
Useful Formula for this Question:
A rhombus satisfies all properties of a parallelogram.
Concept Behind This Question:
Students should understand the hierarchy of quadrilaterals.
Step-by-Step Solution:
A rhombus has:
- Opposite sides parallel.
- Opposite sides equal.
Hence every rhombus is a parallelogram.
The remaining statements are false.
Therefore, the correct answer is:
Every rhombus is a parallelogram.
Exam Tip:
Remember the relationship:
Square ⊂ Rectangle ⊂ Parallelogram
Square ⊂ Rhombus ⊂ Parallelogram
Q5. A regular polygon has $$24$$ sides. What is each interior angle?
A) $$150^\circ$$
B) $$160^\circ$$
C) $$165^\circ$$
D) $$170^\circ$$
Answer:
$$165^\circ$$
Useful Formula for this Question:
$$\frac{(n-2)\times180^\circ}{n}$$
Concept Behind This Question:
Students should calculate the interior angle of a regular polygon.
Step-by-Step Solution:
$$\frac{(24-2)\times180}{24}$$
$$=\frac{22\times180}{24}$$
$$=165^\circ$$
Therefore, the correct answer is:
$$165^\circ$$
Exam Tip:
Interior angles of regular polygons increase as the number of sides increases.
Important Formulas & Concepts
1. Sum of Interior Angles
$$ (n-2)\times180^\circ $$
2. Sum of Exterior Angles
$$360^\circ$$
3. Interior Angle of a Regular Polygon
$$\frac{(n-2)\times180^\circ}{n}$$
4. Exterior Angle of a Regular Polygon
$$\frac{360^\circ}{n}$$
5. Number of Diagonals
$$\frac{n(n-3)}{2}$$
6. Relationship Among Quadrilaterals
- Square ⊂ Rectangle
- Square ⊂ Rhombus
- Rectangle ⊂ Parallelogram
- Rhombus ⊂ Parallelogram
FAQs
1. How do you calculate the interior angle of a regular polygon?
$$\frac{(n-2)\times180^\circ}{n}$$
2. Which polygon has $$90$$ diagonals?
A $$15$$-sided polygon.
3. What is the sum of the exterior angles of every convex polygon?
$$360^\circ$$
4. Is every rhombus a parallelogram?
Yes.
5. Which formula is used to calculate diagonals?
$$\frac{n(n-3)}{2}$$
Common Mistakes
❌ Forgetting to find the number of sides before calculating diagonals.
❌ Confusing interior and exterior angle formulas.
❌ Assuming every rhombus is a square.
❌ Using the wrong polygon formula.
❌ Ignoring algebraic simplification.
Quick Revision Notes
✔ Interior angle sum:
$$ (n-2)\times180^\circ $$
✔ Interior angle of a regular polygon:
$$\frac{(n-2)\times180^\circ}{n}$$
✔ Exterior angle:
$$\frac{360^\circ}{n}$$
✔ Diagonals:
$$\frac{n(n-3)}{2}$$
✔ Every square is both a rectangle and a rhombus.
✔ Every rhombus is a parallelogram.
Conclusion
This HOTS practice set tests students’ conceptual understanding of quadrilaterals through multi-step reasoning and application-based questions. Solving such advanced MCQs regularly improves logical thinking, mathematical accuracy, and confidence for school examinations, Olympiads, and scholarship tests.
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