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Practice Class 8 Maths Chapter 3 Understanding Quadrilaterals MCQ Questions with Answers based on the NCERT latest syllabus. Solve advanced HOTS MCQs on polygons, quadrilaterals, diagonals, interior angles, exterior angles, and special quadrilaterals 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 advanced practice set is designed to strengthen conceptual understanding through higher-order thinking questions. Students must combine multiple concepts such as polygon angle properties, diagonals, and quadrilateral properties to solve these questions accurately.
What You Will Learn?
✔ Interior Angle Sum Applications
✔ Exterior Angle Applications
✔ Diagonal-Based Problems
✔ Regular Polygon Concepts
✔ Properties of Special Quadrilaterals
✔ Logical Geometry Questions
✔ HOTS Practice
Why This Topic Is Important?
Application-based geometry questions improve analytical thinking and prepare students for school exams, Olympiads, and scholarship examinations.
Exam Relevance
These questions are useful for:
✔ CBSE Exams
✔ State Board Exams
✔ Olympiad Preparation
✔ Scholarship Exams
✔ Unit Tests
✔ Annual Exams
Q1. A regular polygon has each exterior angle equal to $$15^\circ$$. The number of diagonals of the polygon is:
A) $$252$$
B) $$270$$
C) $$324$$
D) $$342$$
Answer:
$$252$$
Useful Formula for this Question:
$$n=\frac{360^\circ}{\text{Exterior Angle}}$$
$$D=\frac{n(n-3)}{2}$$
Concept Behind This Question:
Students should first determine the number of sides and then calculate the number of diagonals.
Step-by-Step Solution:
Given,
$$\text{Exterior Angle}=15^\circ$$
$$n=\frac{360}{15}=24$$
Now,
$$D=\frac{24(24-3)}{2}$$
$$=\frac{24\times21}{2}$$
$$=252$$
Therefore, the correct answer is:
$$252$$
Exam Tip:
Read the question carefully. Sometimes more than one formula is required.
Q2. The sum of the interior angles of a polygon is $$2160^\circ$$. How many sides does the polygon have?
A) $$12$$
B) $$13$$
C) $$14$$
D) $$15$$
Answer:
$$14$$
Useful Formula for this Question:
$$\text{Sum of Interior Angles}=(n-2)\times180^\circ$$
Concept Behind This Question:
Students should determine the number of sides from the interior angle sum.
Step-by-Step Solution:
Given,
$$2160=(n-2)\times180$$
$$n-2=12$$
$$n=14$$
Therefore, the correct answer is:
$$14$$
Exam Tip:
Always divide by $$180$$ before solving for $$n$$.
Q3. Which one of the following statements is always true?
A) Every rectangle is a rhombus.
B) Every square is a parallelogram.
C) Every kite is a rectangle.
D) Every trapezium is a square.
Answer:
Every square is a parallelogram.
Useful Formula for this Question:
A square satisfies all the properties of a parallelogram.
Concept Behind This Question:
Students should understand the relationship among quadrilaterals.
Step-by-Step Solution:
A square has two pairs of opposite sides parallel and equal.
Hence, every square is a parallelogram.
The remaining statements are false.
Therefore, the correct answer is:
Every square is a parallelogram.
Exam Tip:
Remember the hierarchy:
Square ⊂ Rectangle ⊂ Parallelogram
Square ⊂ Rhombus ⊂ Parallelogram
Q4. A polygon has $$119$$ diagonals. How many sides does it have?
A) $$16$$
B) $$17$$
C) $$18$$
D) $$19$$
Answer:
$$17$$
Useful Formula for this Question:
$$D=\frac{n(n-3)}{2}$$
Concept Behind This Question:
Students should solve the diagonal equation.
Step-by-Step Solution:
Given,
$$\frac{n(n-3)}{2}=119$$
$$n(n-3)=238$$
$$n^2-3n-238=0$$
$$(n-17)(n+14)=0$$
$$n=17$$
Therefore, the correct answer is:
$$17$$
Exam Tip:
Ignore the negative root because the number of sides cannot be negative.
Q5. A regular polygon has $$18$$ sides. What is the measure of each interior angle?
A) $$150^\circ$$
B) $$155^\circ$$
C) $$160^\circ$$
D) $$165^\circ$$
Answer:
$$160^\circ$$
Useful Formula for this Question:
$$\text{Interior Angle}=\frac{(n-2)\times180^\circ}{n}$$
Concept Behind This Question:
Students should calculate the interior angle of a regular polygon.
Step-by-Step Solution:
For
$$n=18$$
$$\frac{(18-2)\times180}{18}$$
$$=\frac{16\times180}{18}$$
$$=160^\circ$$
Therefore, the correct answer is:
$$160^\circ$$
Exam Tip:
Interior angles 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. Properties of a Square
- Four equal sides.
- Four right angles.
- Opposite sides are parallel.
- Diagonals are equal and bisect each other at right angles.
FAQs
1. What is the sum of the exterior angles of every convex polygon?
$$360^\circ$$
2. Which polygon has $$119$$ diagonals?
A $$17$$-sided polygon.
3. What is the interior angle of a regular 18-sided polygon?
$$160^\circ$$
4. Is every square a parallelogram?
Yes.
5. Which formula is used to calculate diagonals?
$$\frac{n(n-3)}{2}$$
Common Mistakes
❌ Confusing interior angle and exterior angle formulas.
❌ Forgetting to calculate the number of sides before finding diagonals.
❌ Assuming every rectangle is a rhombus.
❌ Ignoring algebraic simplification.
❌ Selecting the negative root while solving quadratic equations.
Quick Revision Notes
✔ Interior angle sum:
$$ (n-2)\times180^\circ $$
✔ Exterior angle sum:
$$360^\circ$$
✔ Interior angle of a regular polygon:
$$\frac{(n-2)\times180^\circ}{n}$$
✔ Number of diagonals:
$$\frac{n(n-3)}{2}$$
✔ Every square is both a rectangle and a rhombus.
✔ Every square is a parallelogram.
Conclusion
This HOTS Practice Set strengthens students’ understanding of polygons and quadrilaterals through challenging, multi-step questions. Regular practice of such concept-based MCQs improves mathematical reasoning, accuracy, and confidence for CBSE examinations and competitive school-level tests.
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