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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 properties, 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. It introduces students to polygons, angle properties, diagonals, and special quadrilaterals. Mastering these concepts helps students solve geometry problems accurately and confidently.
What You Will Learn?
✔ Types of Polygons
✔ Interior Angle Sum Property
✔ Exterior Angle Property
✔ Regular Polygons
✔ Diagonals of Polygons
✔ Properties of Quadrilaterals
✔ Parallelogram, Rectangle, Rhombus and Square
✔ Trapezium
Why This Topic Is Important?
The concepts of quadrilaterals are widely used in architecture, engineering, surveying, design, and construction. Understanding these concepts develops logical reasoning and strengthens geometry skills.
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 14-sided polygon is:
A) $$1980^\circ$$
B) $$2160^\circ$$
C) $$2340^\circ$$
D) $$2520^\circ$$
Answer:
$$2160^\circ$$
Useful Formula for this Question:
$$\text{Sum of Interior Angles}=(n-2)\times180^\circ$$
Concept Behind This Question:
Students should calculate the angle sum of a polygon using the standard formula.
Step-by-Step Solution:
For a 14-sided polygon,
$$n=14$$
$$=(14-2)\times180^\circ$$
$$=12\times180^\circ$$
$$=2160^\circ$$
Therefore, the correct answer is:
$$2160^\circ$$
Exam Tip:
The interior angle sum depends only on the number of sides.
Q2. Which quadrilateral has both pairs of opposite sides parallel and all four sides equal?
A) Rectangle
B) Rhombus
C) Trapezium
D) Kite
Answer:
$$\text{Rhombus}$$
Useful Formula for this Question:
Properties of a rhombus:
- Four equal sides.
- Opposite sides parallel.
- Opposite angles equal.
Concept Behind This Question:
Students should identify the defining properties of a rhombus.
Step-by-Step Solution:
A rhombus has:
- Four equal sides.
- Two pairs of opposite sides parallel.
- Opposite angles equal.
Therefore, the correct answer is:
$$\text{Rhombus}$$
Exam Tip:
A square is a special rhombus in which each angle is $$90^\circ$$.
Q3. A regular polygon has each exterior angle equal to $$15^\circ$$. The number of sides is:
A) $$20$$
B) $$22$$
C) $$24$$
D) $$25$$
Answer:
$$24$$
Useful Formula for this Question:
$$n=\frac{360^\circ}{\text{Exterior Angle}}$$
Concept Behind This Question:
Students should determine the number of sides from the exterior angle.
Step-by-Step Solution:
Given,
$$\text{Exterior Angle}=15^\circ$$
$$n=\frac{360}{15}$$
$$=24$$
Therefore, the polygon has:
$$24$$ sides.
Hence, the correct answer is:
$$24$$
Exam Tip:
The smaller the exterior angle, the greater the number of sides.
Q4. How many diagonals does a 14-sided polygon have?
A) $$70$$
B) $$72$$
C) $$75$$
D) $$77$$
Answer:
$$77$$
Useful Formula for this Question:
$$\frac{n(n-3)}{2}$$
Concept Behind This Question:
Students should apply the diagonal formula accurately.
Step-by-Step Solution:
For a 14-sided polygon,
$$n=14$$
$$\frac{14(14-3)}{2}$$
$$=\frac{14\times11}{2}$$
$$=77$$
Therefore, the correct answer is:
$$77$$
Exam Tip:
Use the formula carefully and simplify before multiplying whenever possible.
Q5. Which statement is always true for a square?
A) Only opposite sides are equal.
B) Only opposite angles are equal.
C) All sides are equal and diagonals are equal.
D) Only one pair of sides is parallel.
Answer:
All sides are equal and diagonals are equal.
Useful Formula for this Question:
Properties of a square:
- Four equal sides.
- Four right angles.
- Equal diagonals.
- Diagonals bisect each other at right angles.
Concept Behind This Question:
Students should identify all the important properties of a square.
Step-by-Step Solution:
A square has:
- Four equal sides.
- Four right angles.
- Equal diagonals.
- Opposite sides parallel.
Therefore, the correct answer is:
All sides are equal and diagonals are equal.
Exam Tip:
A square combines the properties of both a rectangle and a rhombus.
Important Formulas & Concepts
1. Sum of Interior Angles
$$ (n-2)\times180^\circ $$
2. Sum of Exterior Angles
$$360^\circ$$
3. Number of Diagonals
$$\frac{n(n-3)}{2}$$
4. Exterior Angle of a Regular Polygon
$$\frac{360^\circ}{n}$$
5. Properties of a Square
- Four equal sides.
- Four right angles.
- Equal diagonals.
- Diagonals bisect each other at right angles.
6. Properties of a Rhombus
- Four equal sides.
- Opposite sides parallel.
- Opposite angles equal.
FAQs
1. What is the sum of the interior angles of a 14-sided polygon?
$$2160^\circ$$
2. How many diagonals does a 14-sided polygon have?
$$77$$
3. What is the exterior angle of a regular 24-sided polygon?
$$15^\circ$$
4. Which quadrilateral has four equal sides?
A rhombus and a square.
5. What are the properties of a square?
It has four equal sides, four right angles, equal diagonals, and diagonals that bisect each other at right angles.
Common Mistakes
❌ Forgetting to subtract $$2$$ in the interior angle formula.
❌ Using the wrong formula for diagonals.
❌ Confusing a rhombus with a square.
❌ Incorrect calculation of the number of sides.
❌ Forgetting that the exterior angle sum is always $$360^\circ$$.
Quick Revision Notes
✔ Interior angle sum:
$$ (n-2)\times180^\circ $$
✔ Exterior angle sum:
$$360^\circ$$
✔ Number of diagonals:
$$\frac{n(n-3)}{2}$$
✔ Rhombus has four equal sides.
✔ Square has equal sides and equal diagonals.
✔ A regular 24-sided polygon has an exterior angle of $$15^\circ$$.
Conclusion
Understanding Quadrilaterals is an essential chapter in Class 8 Mathematics. A clear understanding of polygons, diagonals, angle properties, and special quadrilaterals helps students solve geometry problems efficiently. Regular MCQ practice strengthens conceptual understanding, improves accuracy, and boosts confidence in examinations.
Related links
- 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
- Class 8 Maths Chapter 2 Linear Equations in One Variable – part 10
- Class 8 Maths Chapter 2 Linear Equations in One Variable – Part 9
- Class 8 Maths Chapter 1 Rational Numbers- Part 10
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