Welcome To My School Study
Practice Class 8 Maths Chapter 3 Understanding Quadrilaterals MCQ Questions with Answers based on the NCERT latest syllabus. Solve HOTS and application-based MCQs on polygons, quadrilaterals, diagonals, angle properties, and regular polygons with detailed step-by-step solutions for CBSE exams.
Do You Know
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 HOTS practice set focuses on advanced applications of polygon and quadrilateral properties. The questions require logical reasoning, multiple-step calculations, and conceptual understanding rather than direct formula application.
What You Will Learn?
✔ Interior Angle Applications
✔ Exterior Angle Applications
✔ Polygon Reasoning
✔ Diagonal Problems
✔ Properties of Special Quadrilaterals
✔ Multi-Step Geometry Questions
✔ Olympiad-Level Thinking
Why This Topic Is Important?
Application-based questions improve analytical ability and prepare students for scholarship exams, Olympiads, and higher-level school examinations.
Exam Relevance
These questions are useful for:
✔ CBSE Exams
✔ State Board Exams
✔ Olympiad Preparation
✔ Scholarship Exams
✔ School Tests
✔ Annual Examinations
Q1. The sum of the interior angles of a polygon is $$2700^\circ$$. How many sides does the polygon have?
A) $$15$$
B) $$16$$
C) $$17$$
D) $$18$$
Answer:
$$17$$
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 given angle sum.
Step-by-Step Solution:
Given,
$$(n-2)\times180=2700$$
$$n-2=15$$
$$n=17$$
Therefore, the correct answer is:
$$17$$
Exam Tip:
First calculate the number of sides, then solve any further question based on it.
Q2. A polygon has $$54$$ diagonals. The number of sides of the polygon is:
A) $$10$$
B) $$11$$
C) $$12$$
D) $$13$$
Answer:
$$12$$
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:
$$\frac{n(n-3)}{2}=54$$
$$n(n-3)=108$$
$$n^2-3n-108=0$$
$$(n-12)(n+9)=0$$
$$n=12$$
Therefore, the correct answer is:
$$12$$
Exam Tip:
Diagonal questions often require solving a quadratic equation.
Q3. Each exterior angle of a regular polygon is $$9^\circ$$. The polygon has:
A) $$36$$ sides
B) $$40$$ sides
C) $$45$$ sides
D) $$48$$ sides
Answer:
$$40$$
Useful Formula for this Question:
$$\text{Exterior Angle}=\frac{360^\circ}{n}$$
Concept Behind This Question:
Students should determine the number of sides using the exterior angle.
Step-by-Step Solution:
$$n=\frac{360}{9}$$
$$=40$$
Therefore, the correct answer is:
$$40$$
Exam Tip:
A smaller exterior angle means a polygon with more sides.
Q4. Which one of the following quadrilaterals always has perpendicular diagonals but does not necessarily have equal diagonals?
A) Rectangle
B) Rhombus
C) Parallelogram
D) Trapezium
Answer:
$$\text{Rhombus}$$
Useful Formula for this Question:
Properties of a rhombus:
- Diagonals bisect each other.
- Diagonals are perpendicular.
Concept Behind This Question:
Students should distinguish between the diagonal properties of different quadrilaterals.
Step-by-Step Solution:
A rhombus always has perpendicular diagonals.
However, its diagonals are generally not equal.
Therefore, the correct answer is:
$$\text{Rhombus}$$
Exam Tip:
Only a square has diagonals that are both equal and perpendicular.
Q5. A regular polygon has $$45$$ diagonals. How many sides does it have?
A) $$9$$
B) $$10$$
C) $$11$$
D) $$12$$
Answer:
$$10$$
Useful Formula for this Question:
$$D=\frac{n(n-3)}{2}$$
Concept Behind This Question:
Students should calculate the number of sides from the number of diagonals.
Step-by-Step Solution:
$$\frac{n(n-3)}{2}=45$$
$$n(n-3)=90$$
$$n^2-3n-90=0$$
$$(n-10)(n+9)=0$$
$$n=10$$
Therefore, the correct answer is:
$$10$$
Exam Tip:
Memorize common diagonal values for polygons to solve questions faster.
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 Rhombus
- Four equal sides.
- Opposite sides are parallel.
- Opposite angles are equal.
- Diagonals bisect each other at right angles.
FAQs
1. What is the sum of the exterior angles of a convex polygon?
$$360^\circ$$
2. Which polygon has $$54$$ diagonals?
A $$12$$-sided polygon.
3. Which quadrilateral always has perpendicular diagonals?
A rhombus and a square.
4. How do you calculate the number of diagonals?
$$\frac{n(n-3)}{2}$$
5. A regular polygon has an exterior angle of $$9^\circ$$. How many sides does it have?
$$40$$ sides.
Common Mistakes
❌ Mixing up interior and exterior angle formulas.
❌ Forgetting to simplify the quadratic equation.
❌ Assuming all quadrilaterals have equal diagonals.
❌ Confusing a rhombus with a square.
❌ Using the wrong value of $$n$$ in formulas.
Quick Revision Notes
✔ Interior angle sum:
$$ (n-2)\times180^\circ $$
✔ Exterior angle sum:
$$360^\circ$$
✔ Interior angle of a regular polygon:
$$\frac{(n-2)\times180^\circ}{n}$$
✔ Exterior angle:
$$\frac{360^\circ}{n}$$
✔ Number of diagonals:
$$\frac{n(n-3)}{2}$$
✔ A square has diagonals that are equal as well as perpendicular.
Conclusion
This HOTS practice set helps students strengthen their understanding of quadrilaterals through reasoning-based and multi-step problems. Regular practice of such advanced questions improves analytical thinking, problem-solving speed, and confidence for CBSE exams, Olympiads, and scholarship examinations.
Related links
- Class 8 Science Chapter 1 Crop Production and Management
- Class 8 Social Science Chapter 1 How, When and Where
- Class 8 Science Chapter 1 Crop Production and Management
- Class 8 Maths Chapter 3 Understanding Quadrilaterals part-13
- Class 8 Maths Chapter 3 Understanding Quadrilaterals part-12
- Class 8 Maths Chapter 3 Understanding Quadrilaterals part-11
- Class 8 Maths Chapter 3 Understanding Quadrilaterals part-9
- Class 8 Maths Chapter 3 Understanding Quadrilaterals part-8
- Class 8 Maths Chapter 3 Understanding Quadrilaterals part-7
- Class 8 Maths Chapter 3 Understanding Quadrilaterals part-6
- Class 8 Maths Chapter 3 Understanding Quadrilaterals part-5
- Class 8 Maths Chapter 3 Understanding Quadrilaterals part-4
Latest Posts
- Class 9 Maths Chapter 4 Linear Equations in Two Variables
- Class 7 Maths Chapter 4 Simple Equations
- Class 8 Maths Chapter 4 Practical Geometry
- Class 10 Maths Chapter 4 Quadratic Equations
- Class 9 Science Chapter 1 Matter in Our Surroundings
Join Our Other Communities
Instagram , Youtube , Facebook
