Welcome To My School Study
Practice Class 8 Maths Chapter 3 Understanding Quadrilaterals MCQ Questions with Answers based on NCERT syllabus. Learn polygons, quadrilaterals, angle sum property, diagonals, regular polygons, parallelogram, rectangle, square, rhombus, and trapezium with detailed solutions for CBSE exams.
Do You Know
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 helps students understand different types of polygons and their properties. This chapter strengthens geometrical concepts and develops logical reasoning, which are essential for higher mathematics.
What You Will Learn?
✔ Polygons
✔ Quadrilaterals
✔ Interior Angle Sum Property
✔ Exterior Angle Property
✔ Diagonals
✔ Regular Polygons
✔ Parallelogram
✔ Rectangle, Square, Rhombus and Trapezium
Why This Topic Is Important?
The concepts of quadrilaterals are widely used in engineering, architecture, construction, surveying, and computer graphics. Understanding these concepts helps students solve geometry problems effectively.
Exam Relevance
These questions are useful for:
✔ CBSE Exams
✔ State Board Exams
✔ School Tests
✔ Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
Q1. A regular pentagon has each exterior angle equal to:
A) $$60^\circ$$
B) $$72^\circ$$
C) $$90^\circ$$
D) $$108^\circ$$
Answer:
$$72^\circ$$
Useful Formula for this Question:
For a regular polygon,
$$\text{Exterior Angle}=\frac{360^\circ}{n}$$
Concept Behind This Question:
Students should calculate the exterior angle of a regular polygon.
Step-by-Step Solution:
For a regular pentagon,
$$n=5$$
$$\frac{360^\circ}{5}=72^\circ$$
Therefore, the correct answer is:
$$72^\circ$$
Exam Tip:
Exterior angle is calculated only for regular polygons.
Q2. Which quadrilateral always has diagonals of equal length?
A) Rhombus
B) Rectangle
C) Kite
D) Trapezium
Answer:
$$\text{Rectangle}$$
Useful Formula for this Question:
In a rectangle:
- Diagonals are equal.
- Diagonals bisect each other.
Concept Behind This Question:
Students should know the diagonal properties of a rectangle.
Step-by-Step Solution:
The diagonals of a rectangle are always equal in length.
A rhombus does not always have equal diagonals.
Therefore, the correct answer is:
$$\text{Rectangle}$$
Exam Tip:
A square also has equal diagonals because it is a special rectangle.
Q3. The sum of the interior angles of a nonagon is:
A) $$1080^\circ$$
B) $$1260^\circ$$
C) $$1440^\circ$$
D) $$1620^\circ$$
Answer:
$$1260^\circ$$
Useful Formula for this Question:
$$\text{Sum of Interior Angles}=(n-2)\times180^\circ$$
Concept Behind This Question:
Students should use the polygon angle sum formula.
Step-by-Step Solution:
For a nonagon,
$$n=9$$
$$=(9-2)\times180^\circ$$
$$=7\times180^\circ$$
$$=1260^\circ$$
Therefore, the correct answer is:
$$1260^\circ$$
Exam Tip:
Always subtract $$2$$ from the number of sides first.
Q4. Which quadrilateral has all sides equal and all angles equal?
A) Rhombus
B) Rectangle
C) Square
D) Kite
Answer:
$$\text{Square}$$
Useful Formula for this Question:
Properties of a square:
- All sides are equal.
- All angles are $$90^\circ$$.
Concept Behind This Question:
Students should identify the complete properties of a square.
Step-by-Step Solution:
A square satisfies both conditions:
- Four equal sides.
- Four equal right angles.
Therefore, the correct answer is:
$$\text{Square}$$
Exam Tip:
A square is both a rectangle and a rhombus.
Q5. How many diagonals does a decagon have?
A) $$30$$
B) $$35$$
C) $$40$$
D) $$45$$
Answer:
$$35$$
Useful Formula for this Question:
$$\text{Number of Diagonals}=\frac{n(n-3)}{2}$$
Concept Behind This Question:
Students should calculate diagonals using the standard formula.
Step-by-Step Solution:
For a decagon,
$$n=10$$
$$\frac{10(10-3)}{2}$$
$$=\frac{10\times7}{2}$$
$$=35$$
Therefore, the correct answer is:
$$35$$
Exam Tip:
Memorize the diagonal formula to solve such questions quickly.
Important Formulas & Concepts
1. Sum of Interior Angles of a Polygon
$$ (n-2)\times180^\circ $$
2. Sum of Exterior Angles of Any 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.
- Diagonals are equal.
6. Properties of a Square
- Four equal sides.
- Four right angles.
- Equal diagonals that bisect each other.
FAQs
1. What is the exterior angle of a regular pentagon?
$$72^\circ$$
2. Which quadrilateral has equal sides and equal angles?
A square.
3. How many diagonals does a decagon have?
$$35$$
4. What is the angle sum of a nonagon?
$$1260^\circ$$
5. Which quadrilateral always has equal diagonals?
A rectangle and a square.
Common Mistakes
❌ Confusing a square with a rhombus.
❌ Using the wrong formula for diagonals.
❌ Forgetting that exterior angles total $$360^\circ$$.
❌ Incorrect calculation of polygon angle sums.
❌ Assuming all rhombuses have equal diagonals.
Quick Revision Notes
✔ Regular pentagon exterior angle is $$72^\circ$$.
✔ Nonagon angle sum is $$1260^\circ$$.
✔ Decagon has $$35$$ diagonals.
✔ Rectangle has equal diagonals.
✔ Square has equal sides and equal angles.
✔ Exterior angles of every polygon add up to $$360^\circ$$.
Conclusion
Understanding Quadrilaterals is an important chapter in Class 8 Mathematics. Learning the properties of polygons, diagonals, and special quadrilaterals helps students solve geometry questions efficiently. Regular MCQ practice improves conceptual understanding, logical reasoning, and examination performance.
Related links
- 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 3 Understanding Quadrilaterals angle sum property
- Class 8 Maths Chapter 3 Understanding Quadrilaterals part-2
- Class 8 Maths Chapter 3 Understanding Quadrilaterals part-1
- 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
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
