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Practice Class 8 Maths Chapter 3 Understanding Quadrilaterals MCQ Questions with Answers based on NCERT syllabus. Learn polygons, quadrilaterals, angle sum property, exterior angles, diagonals, 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 geometry chapter that explains the properties of polygons and different quadrilaterals. It helps students develop logical thinking and strengthens their understanding of geometrical concepts.
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 commonly used in architecture, construction, engineering, map-making, and design. Learning their properties improves problem-solving skills and prepares students for higher mathematics.
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 heptagon is:
A) $$720^\circ$$
B) $$900^\circ$$
C) $$1080^\circ$$
D) $$1260^\circ$$
Answer:
$$900^\circ$$
Useful Formula for this Question:
$$\text{Sum of Interior Angles}=(n-2)\times180^\circ$$
Concept Behind This Question:
Students should use the interior angle sum formula for polygons.
Step-by-Step Solution:
For a heptagon,
$$n=7$$
$$=(7-2)\times180^\circ$$
$$=5\times180^\circ$$
$$=900^\circ$$
Therefore, the correct answer is:
$$900^\circ$$
Exam Tip:
A heptagon has $$7$$ sides.
Q2. Which quadrilateral has exactly one pair of opposite sides parallel?
A) Rectangle
B) Rhombus
C) Trapezium
D) Square
Answer:
$$\text{Trapezium}$$
Useful Formula for this Question:
A trapezium has exactly one pair of opposite sides parallel.
Concept Behind This Question:
Students should identify the properties of different quadrilaterals.
Step-by-Step Solution:
A trapezium has one pair of opposite sides parallel, while the other pair is not parallel.
Therefore, the correct answer is:
$$\text{Trapezium}$$
Exam Tip:
Do not confuse a trapezium with a parallelogram, which has two pairs of parallel sides.
Q3. How many diagonals does a nonagon have?
A) $$24$$
B) $$25$$
C) $$26$$
D) $$27$$
Answer:
$$27$$
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 a nonagon,
$$n=9$$
$$\frac{9(9-3)}{2}$$
$$=\frac{9\times6}{2}$$
$$=27$$
Therefore, the correct answer is:
$$27$$
Exam Tip:
Remember the diagonal formula for all polygons.
Q4. Each exterior angle of a regular decagon is:
A) $$30^\circ$$
B) $$36^\circ$$
C) $$40^\circ$$
D) $$45^\circ$$
Answer:
$$36^\circ$$
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 decagon,
$$n=10$$
$$\frac{360^\circ}{10}$$
$$=36^\circ$$
Therefore, the correct answer is:
$$36^\circ$$
Exam Tip:
This formula is applicable only to regular polygons.
Q5. Which of the following statements is true for a parallelogram?
A) Adjacent sides are always equal.
B) Opposite sides are equal and parallel.
C) All angles are $$90^\circ$$.
D) All sides are equal.
Answer:
Opposite sides are equal and parallel.
Useful Formula for this Question:
Properties of a parallelogram:
- Opposite sides are equal.
- Opposite sides are parallel.
Concept Behind This Question:
Students should identify the correct properties of a parallelogram.
Step-by-Step Solution:
A parallelogram always has:
- Opposite sides equal.
- Opposite sides parallel.
- Opposite angles equal.
It does not necessarily have four right angles or four equal sides.
Therefore, the correct answer is:
Opposite sides are equal and parallel.
Exam Tip:
Rectangle, rhombus, and square are all special types of parallelograms.
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.
- Diagonals bisect each other.
6. Properties of a Trapezium
- Exactly one pair of opposite sides is parallel.
FAQs
1. What is the sum of the interior angles of a heptagon?
$$900^\circ$$
2. How many diagonals does a nonagon have?
$$27$$
3. Which quadrilateral has one pair of parallel sides?
A trapezium.
4. What is the exterior angle of a regular decagon?
$$36^\circ$$
5. What are the basic properties of a parallelogram?
Opposite sides are equal and parallel, opposite angles are equal, and diagonals bisect each other.
Common Mistakes
❌ Using the wrong value of $$n$$ in formulas.
❌ Confusing a trapezium with a parallelogram.
❌ Forgetting the diagonal formula.
❌ Assuming every parallelogram has four right angles.
❌ Incorrect calculation of exterior angles.
Quick Revision Notes
✔ Heptagon angle sum is $$900^\circ$$.
✔ Nonagon has $$27$$ diagonals.
✔ Trapezium has one pair of parallel sides.
✔ Parallelogram has opposite sides equal and parallel.
✔ Exterior angle of a regular decagon is $$36^\circ$$.
✔ Exterior angles of every polygon add up to $$360^\circ$$.
Conclusion
Understanding Quadrilaterals is a fundamental chapter in Class 8 Mathematics. A clear understanding of polygon properties, diagonals, angle sums, and special quadrilaterals helps students solve geometry problems confidently. Regular MCQ practice improves conceptual understanding, logical reasoning, and exam performance.
Related links
- 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
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