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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 introduces students to the properties of polygons and special quadrilaterals. These concepts form the basis of geometry and help students solve problems related to angles, diagonals, and different geometric shapes.
What You Will Learn?
✔ Types of Polygons
✔ Angle Sum Property
✔ Exterior Angle Property
✔ Regular Polygons
✔ Diagonals of Polygons
✔ Parallelogram
✔ Rectangle
✔ Square, Rhombus and Trapezium
Why This Topic Is Important?
Quadrilaterals are widely used in engineering, architecture, construction, and design. Understanding their properties strengthens mathematical thinking and problem-solving 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 exterior angles of any convex polygon is:
A) $$90^\circ$$
B) $$180^\circ$$
C) $$270^\circ$$
D) $$360^\circ$$
Answer:
$$360^\circ$$
Useful Formula for this Question:
For every convex polygon,
$$\text{Sum of Exterior Angles}=360^\circ$$
Concept Behind This Question:
Students should remember the exterior angle property of polygons.
Step-by-Step Solution:
Regardless of the number of sides, the sum of one exterior angle at each vertex of a convex polygon is always:
$$360^\circ$$
Therefore, the correct answer is:
$$360^\circ$$
Exam Tip:
This property is true for all convex polygons.
Q2. A regular polygon has 9 sides. Each exterior angle measures:
A) $$30^\circ$$
B) $$36^\circ$$
C) $$40^\circ$$
D) $$45^\circ$$
Answer:
$$40^\circ$$
Useful Formula for this Question:
$$\text{Exterior Angle}=\frac{360^\circ}{n}$$
Concept Behind This Question:
Students should calculate the exterior angle of a regular polygon.
Step-by-Step Solution:
For a regular nonagon,
$$n=9$$
$$\frac{360^\circ}{9}=40^\circ$$
Therefore, the correct answer is:
$$40^\circ$$
Exam Tip:
Exterior angle decreases as the number of sides increases.
Q3. Which quadrilateral always has opposite angles equal?
A) Kite
B) Trapezium
C) Parallelogram
D) Pentagon
Answer:
$$\text{Parallelogram}$$
Useful Formula for this Question:
Properties of a parallelogram:
- Opposite sides are parallel.
- Opposite sides are equal.
- Opposite angles are equal.
Concept Behind This Question:
Students should identify the angle properties of a parallelogram.
Step-by-Step Solution:
In every parallelogram,
- Opposite angles are equal.
- Adjacent angles are supplementary.
Therefore, the correct answer is:
$$\text{Parallelogram}$$
Exam Tip:
Adjacent angles of a parallelogram always add up to $$180^\circ$$.
Q4. How many diagonals does an 11-sided polygon have?
A) $$40$$
B) $$42$$
C) $$44$$
D) $$46$$
Answer:
$$44$$
Useful Formula for this Question:
$$\frac{n(n-3)}{2}$$
Concept Behind This Question:
Students should apply the diagonal formula correctly.
Step-by-Step Solution:
For an 11-sided polygon,
$$n=11$$
$$\frac{11(11-3)}{2}$$
$$=\frac{11\times8}{2}$$
$$=44$$
Therefore, the correct answer is:
$$44$$
Exam Tip:
Subtract $$3$$ from the number of sides before multiplying.
Q5. Which quadrilateral has all four sides equal but its angles are not necessarily $$90^\circ$$?
A) Rectangle
B) Square
C) Rhombus
D) Trapezium
Answer:
$$\text{Rhombus}$$
Useful Formula for this Question:
Properties of a rhombus:
- Four equal sides.
- Opposite angles are equal.
Concept Behind This Question:
Students should distinguish between a rhombus and a square.
Step-by-Step Solution:
A rhombus always has four equal sides, but its angles need not be right angles.
Therefore, the correct answer is:
$$\text{Rhombus}$$
Exam Tip:
Every square is a rhombus, but every rhombus is not a square.
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 Parallelogram
- Opposite sides are parallel.
- Opposite sides are equal.
- Opposite angles are equal.
- Diagonals bisect each other.
6. Properties of a Rhombus
- Four equal sides.
- Opposite angles are equal.
- Diagonals bisect each other at right angles.
FAQs
1. What is the sum of the exterior angles of a polygon?
$$360^\circ$$
2. How many diagonals does an 11-sided polygon have?
$$44$$
3. Which quadrilateral has four equal sides but not necessarily right angles?
A rhombus.
4. What is the exterior angle of a regular nonagon?
$$40^\circ$$
5. Which quadrilateral always has opposite angles equal?
A parallelogram.
Common Mistakes
❌ Confusing a rhombus with a square.
❌ Forgetting that exterior angles always total $$360^\circ$$.
❌ Using the wrong formula for diagonals.
❌ Assuming all quadrilaterals have right angles.
❌ Incorrect calculation of regular polygon angles.
Quick Revision Notes
✔ Exterior angle sum is always $$360^\circ$$.
✔ A regular nonagon has exterior angle $$40^\circ$$.
✔ A parallelogram has equal opposite angles.
✔ A rhombus has four equal sides.
✔ An 11-sided polygon has $$44$$ diagonals.
✔ Use:
$$\frac{n(n-3)}{2}$$
to calculate diagonals.
Conclusion
Understanding Quadrilaterals is an essential chapter in Class 8 Mathematics. Mastering the properties of polygons, diagonals, and special quadrilaterals helps students solve geometry problems quickly and accurately. Regular MCQ practice improves conceptual understanding, logical reasoning, and exam performance.
Related links
- 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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