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Practice Class 8 Maths Chapter 3 Understanding Quadrilaterals MCQ Questions with Answers based on the NCERT latest syllabus. Learn polygons, quadrilaterals, angle sum property, diagonals, regular polygons, parallelograms, rectangles, squares, rhombuses, and trapeziums with detailed 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: Moderate to Difficult
Based On: NCERT Latest Syllabus
Introduction:
Understanding Quadrilaterals is one of the most important geometry chapters in Class 8 Mathematics. This chapter explains polygons, quadrilaterals, angle properties, diagonals, and the characteristics of special quadrilaterals. Regular practice of concept-based MCQs helps students improve accuracy, logical reasoning, and exam performance.
What You Will Learn?
✔ Types of Polygons
✔ Interior Angle Sum Property
✔ Exterior Angle Property
✔ Regular Polygons
✔ Number of Diagonals
✔ Properties of Parallelogram
✔ Rectangle, Rhombus, Square and Trapezium
✔ Application-Based Geometry Questions
Why This Topic Is Important?
Quadrilaterals are used in architecture, engineering, construction, map-making, and computer graphics. Understanding their properties builds a strong foundation for higher geometry and practical problem-solving.
Exam Relevance
These questions are useful for:
✔ CBSE Exams
✔ State Board Exams
✔ School Tests
✔ Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
Q1. The sum of the interior angles of a 20-sided polygon is:
A) $$3060^\circ$$
B) $$3240^\circ$$
C) $$3420^\circ$$
D) $$3600^\circ$$
Answer:
$$3240^\circ$$
Useful Formula for this Question:
$$\text{Sum of Interior Angles}=(n-2)\times180^\circ$$
Concept Behind This Question:
Students should calculate the interior angle sum of a polygon.
Step-by-Step Solution:
For a 20-sided polygon,
$$n=20$$
$$=(20-2)\times180^\circ$$
$$=18\times180^\circ$$
$$=3240^\circ$$
Therefore, the correct answer is:
$$3240^\circ$$
Exam Tip:
Always subtract $$2$$ from the number of sides before multiplying by $$180^\circ$$.
Q2. A regular polygon has each exterior angle equal to $$10^\circ$$. How many sides does it have?
A) $$30$$
B) $$32$$
C) $$36$$
D) $$40$$
Answer:
$$36$$
Useful Formula for this Question:
$$n=\frac{360^\circ}{\text{Exterior Angle}}$$
Concept Behind This Question:
Students should determine the number of sides of a regular polygon.
Step-by-Step Solution:
Given,
$$\text{Exterior Angle}=10^\circ$$
$$n=\frac{360}{10}$$
$$=36$$
Therefore, the polygon has:
$$36$$ sides.
Hence, the correct answer is:
$$36$$
Exam Tip:
The smaller the exterior angle, the greater the number of sides.
Q3. How many diagonals does an 18-sided polygon have?
A) $$120$$
B) $$125$$
C) $$135$$
D) $$140$$
Answer:
$$135$$
Useful Formula for this Question:
$$\text{Number of Diagonals}=\frac{n(n-3)}{2}$$
Concept Behind This Question:
Students should calculate the number of diagonals using the standard formula.
Step-by-Step Solution:
For an 18-sided polygon,
$$n=18$$
$$\frac{18(18-3)}{2}$$
$$=\frac{18\times15}{2}$$
$$=135$$
Therefore, the correct answer is:
$$135$$
Exam Tip:
Use the diagonal formula carefully and simplify before multiplying.
Q4. Which of the following statements is always true?
A) Every parallelogram is a rectangle.
B) Every rectangle is a square.
C) Every square is a parallelogram.
D) Every trapezium is a rectangle.
Answer:
Every square is a parallelogram.
Useful Formula for this Question:
Properties of a parallelogram:
- Opposite sides are parallel.
- Opposite sides are equal.
A square satisfies all these properties.
Concept Behind This Question:
Students should understand the relationship among different quadrilaterals.
Step-by-Step Solution:
A square has two pairs of opposite sides parallel and equal.
Therefore, every square is a parallelogram.
The other statements are incorrect.
Hence, the correct answer is:
Every square is a parallelogram.
Exam Tip:
Remember:
Square → Rectangle → Parallelogram
and
Square → Rhombus → Parallelogram
Q5. Which quadrilateral always has diagonals that are equal and bisect each other?
A) Rhombus
B) Rectangle
C) Kite
D) Trapezium
Answer:
$$\text{Rectangle}$$
Useful Formula for this Question:
Properties of a rectangle:
- Opposite sides are equal.
- Diagonals are equal.
- Diagonals bisect each other.
Concept Behind This Question:
Students should identify the diagonal properties of different quadrilaterals.
Step-by-Step Solution:
In a rectangle,
- The diagonals are equal.
- The diagonals bisect each other.
A rhombus has diagonals that bisect each other but they are not always equal.
Therefore, the correct answer is:
$$\text{Rectangle}$$
Exam Tip:
A square also has equal diagonals because it is a special rectangle.
Important Formulas & Concepts
1. Sum of Interior Angles of a Polygon
$$ (n-2)\times180^\circ $$
2. Sum of Exterior Angles of Any Convex Polygon
$$360^\circ$$
3. Number of Diagonals
$$\frac{n(n-3)}{2}$$
4. Exterior Angle of a Regular Polygon
$$\frac{360^\circ}{n}$$
5. Properties of a Rectangle
- Opposite sides are equal.
- Opposite sides are parallel.
- Four right angles.
- Equal diagonals that bisect each other.
6. Properties of a Square
- Four equal sides.
- Four right angles.
- Equal diagonals.
- Diagonals bisect each other at right angles.
FAQs
1. What is the sum of the interior angles of a 20-sided polygon?
$$3240^\circ$$
2. How many sides does a regular polygon with an exterior angle of $$10^\circ$$ have?
$$36$$
3. How many diagonals does an 18-sided polygon have?
$$135$$
4. Which quadrilateral has equal diagonals that bisect each other?
A rectangle and a square.
5. Is every square a parallelogram?
Yes. Every square has two pairs of opposite sides parallel.
Common Mistakes
❌ Forgetting that exterior angles always add up to $$360^\circ$$.
❌ Confusing a rhombus with a rectangle.
❌ Using an incorrect value of $$n$$ in formulas.
❌ Forgetting to simplify while calculating diagonals.
❌ Assuming every parallelogram has equal diagonals.
Quick Revision Notes
✔ Interior angle sum:
$$ (n-2)\times180^\circ $$
✔ Exterior angle sum:
$$360^\circ$$
✔ Number of diagonals:
$$\frac{n(n-3)}{2}$$
✔ Rectangle has equal diagonals.
✔ Square is both a rectangle and a rhombus.
✔ A regular polygon with an exterior angle of $$10^\circ$$ has $$36$$ sides.
Conclusion
Understanding Quadrilaterals is a fundamental chapter in Class 8 Mathematics. A strong understanding of polygons, angle properties, diagonals, and the characteristics of special quadrilaterals enables students to solve geometry problems confidently. Regular MCQ practice enhances conceptual understanding, logical reasoning, and examination success.
Related links
- 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
- Class 8 Maths Chapter 3 Understanding Quadrilaterals part-3
- Class 8 Maths Chapter 2 Linear Equations in One Variable part-11
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