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Practice Class 8 Maths Chapter 3 Understanding Quadrilaterals MCQ Questions with Answers based on NCERT syllabus. Learn polygons, quadrilaterals, diagonals, angle sum property, exterior angles, parallelogram, rectangle, square, rhombus, and trapezium 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 an important chapter of Class 8 Mathematics that explains the properties of polygons and different types of quadrilaterals. A strong understanding of this chapter helps students solve geometry questions quickly and accurately.
What You Will Learn?
✔ Polygons
✔ Quadrilaterals
✔ Interior Angle Sum Property
✔ Exterior Angle Property
✔ Diagonals
✔ Parallelogram
✔ Rectangle
✔ Square, Rhombus and Trapezium
Why This Topic Is Important?
Quadrilaterals are used in architecture, engineering, surveying, map design, and everyday geometry. Learning their properties strengthens logical reasoning and prepares students for advanced geometry.
Exam Relevance
These questions are useful for:
✔ CBSE Exams
✔ State Board Exams
✔ School Tests
✔ Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
Q1. How many diagonals does an octagon have?
A) $$16$$
B) $$18$$
C) $$20$$
D) $$22$$
Answer:
$$20$$
Useful Formula for this Question:
Number of diagonals of a polygon:
$$\frac{n(n-3)}{2}$$
Concept Behind This Question:
Students should calculate the number of diagonals using the standard formula.
Step-by-Step Solution:
For an octagon,
$$n=8$$
Using the formula,
$$\frac{8(8-3)}{2}$$
$$=\frac{8\times5}{2}$$
$$=20$$
Therefore, the correct answer is:
$$20$$
Exam Tip:
Memorize the diagonal formula for all polygons.
Q2. Which quadrilateral has both pairs of opposite sides parallel?
A) Kite
B) Trapezium
C) Parallelogram
D) Pentagon
Answer:
$$\text{Parallelogram}$$
Useful Formula for this Question:
A parallelogram has:
- Two pairs of opposite sides parallel.
Concept Behind This Question:
Students should identify the defining property of a parallelogram.
Step-by-Step Solution:
In a parallelogram:
- Opposite sides are parallel.
- Opposite sides are equal.
- Opposite angles are equal.
Therefore, the correct answer is:
$$\text{Parallelogram}$$
Exam Tip:
A rectangle, rhombus, and square are special types of parallelograms.
Q3. Find the sum of the interior angles of a decagon.
A) $$1260^\circ$$
B) $$1440^\circ$$
C) $$1620^\circ$$
D) $$1800^\circ$$
Answer:
$$1440^\circ$$
Useful Formula for this Question:
$$ (n-2)\times180^\circ $$
Concept Behind This Question:
Students should apply the interior angle sum formula correctly.
Step-by-Step Solution:
For a decagon,
$$n=10$$
$$ (10-2)\times180^\circ $$
$$=8\times180^\circ$$
$$=1440^\circ$$
Therefore, the correct answer is:
$$1440^\circ$$
Exam Tip:
Subtract $$2$$ from the number of sides before multiplying by $$180^\circ$$.
Q4. A regular polygon has each exterior angle equal to $$30^\circ$$. How many sides does it have?
A) $$10$$
B) $$11$$
C) $$12$$
D) $$14$$
Answer:
$$12$$
Useful Formula for this Question:
$$n=\frac{360^\circ}{\text{Exterior Angle}}$$
Concept Behind This Question:
Students should determine the number of sides using the exterior angle.
Step-by-Step Solution:
Given:
$$\text{Exterior Angle}=30^\circ$$
Therefore,
$$n=\frac{360}{30}$$
$$=12$$
Hence, the polygon has:
$$12$$ sides.
Therefore, the correct answer is:
$$12$$
Exam Tip:
Always divide $$360^\circ$$ by the exterior angle of a regular polygon.
Q5. Which quadrilateral 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.
- Opposite sides are parallel.
- Diagonals are equal and bisect each other.
Concept Behind This Question:
Students should know the properties of the diagonals of a rectangle.
Step-by-Step Solution:
A rectangle has:
- Four right angles.
- Equal diagonals.
- Diagonals bisect each other.
Therefore, the correct answer is:
$$\text{Rectangle}$$
Exam Tip:
In a square, the diagonals are also equal and bisect each other at right angles.
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 Parallelogram
- Opposite sides are equal.
- Opposite sides are parallel.
- Opposite angles are equal.
6. Properties of a Rectangle
- Four right angles.
- Opposite sides are equal.
- Diagonals are equal and bisect each other.
FAQs
1. How many diagonals does an octagon have?
$$20$$
2. What is the angle sum of a decagon?
$$1440^\circ$$
3. Which quadrilateral has opposite sides parallel?
A parallelogram.
4. How do you find the number of sides of a regular polygon?
Use:
$$n=\frac{360^\circ}{\text{Exterior Angle}}$$
5. Which quadrilateral has equal diagonals?
A rectangle and a square.
Common Mistakes
❌ Forgetting the diagonal formula.
❌ Confusing a rectangle with a rhombus.
❌ Using the wrong value of $$n$$.
❌ Incorrectly calculating exterior angles.
❌ Forgetting that all exterior angles add up to $$360^\circ$$.
Quick Revision Notes
✔ Octagon has $$20$$ diagonals.
✔ Decagon angle sum is $$1440^\circ$$.
✔ Parallelogram has opposite sides parallel.
✔ Rectangle has equal diagonals.
✔ Exterior angle sum is always $$360^\circ$$.
✔ Number of sides of a regular polygon:
$$n=\frac{360^\circ}{\text{Exterior Angle}}$$
Conclusion
Understanding Quadrilaterals is an important chapter in Class 8 Mathematics. Learning the properties of polygons, quadrilaterals, and their diagonals helps students solve geometry problems accurately. Regular MCQ practice improves conceptual understanding, logical reasoning, and examination performance.
Related links
- 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 2 Linear Equations in One Variable transposition method- Part 5
- Class 8 Maths Chapter 2 Linear Equations in One Variable – Part 4
- Class8 Maths Chapter2 Transposition method, variables – Part 3
- Class 8 Maths Chapter 1 Rational Numbers- Part 10
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