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Practice Class 8 Maths Chapter 3 Understanding Quadrilaterals MCQ Questions with Answers based on NCERT syllabus. Learn angle properties, regular polygons, diagonals, quadrilaterals, parallelogram, 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 a fundamental geometry chapter that introduces students to polygons, quadrilaterals, and their important properties. These concepts are essential for solving geometrical problems and preparing for higher mathematics.
What You Will Learn?
✔ Polygons
✔ Quadrilaterals
✔ Interior Angle Sum Property
✔ Exterior Angle Property
✔ Diagonals
✔ Rhombus
✔ Trapezium
✔ Regular Polygons
Why This Topic Is Important?
The properties of quadrilaterals are widely used in geometry, architecture, engineering, and design. A clear understanding of these concepts helps students solve mathematical problems accurately.
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 a hexagon have?
A) $$6$$
B) $$7$$
C) $$8$$
D) $$9$$
Answer:
$$9$$
Useful Formula for this Question:
Number of diagonals of a polygon:
$$\frac{n(n-3)}{2}$$
Concept Behind This Question:
Students should apply the diagonal formula correctly.
Step-by-Step Solution:
For a hexagon,
$$n=6$$
$$\frac{6(6-3)}{2}$$
$$=\frac{6\times3}{2}$$
$$=9$$
Therefore, the correct answer is:
$$9$$
Exam Tip:
Always substitute the correct value of $$n$$ before solving.
Q2. Which quadrilateral has all sides equal and opposite angles equal?
A) Rectangle
B) Rhombus
C) Trapezium
D) Kite
Answer:
$$\text{Rhombus}$$
Useful Formula for this Question:
Properties of a rhombus:
- All sides are equal.
- Opposite angles are equal.
Concept Behind This Question:
Students should identify the properties of a rhombus.
Step-by-Step Solution:
A rhombus has:
- Four equal sides.
- Opposite sides parallel.
- Opposite angles equal.
Therefore, the correct answer is:
$$\text{Rhombus}$$
Exam Tip:
A square is a special type of rhombus having all angles equal to $$90^\circ$$.
Q3. Find the sum of the interior angles of an octagon.
A) $$900^\circ$$
B) $$960^\circ$$
C) $$1080^\circ$$
D) $$1260^\circ$$
Answer:
$$1080^\circ$$
Useful Formula for this Question:
$$ (n-2)\times180^\circ $$
Concept Behind This Question:
Students should calculate the angle sum of polygons.
Step-by-Step Solution:
For an octagon,
$$n=8$$
$$ (8-2)\times180^\circ $$
$$=6\times180^\circ$$
$$=1080^\circ$$
Therefore, the correct answer is:
$$1080^\circ$$
Exam Tip:
Subtract $$2$$ from the number of sides before multiplying by $$180^\circ$$.
Q4. A regular hexagon has each exterior angle equal to:
A) $$45^\circ$$
B) $$60^\circ$$
C) $$72^\circ$$
D) $$90^\circ$$
Answer:
$$60^\circ$$
Useful Formula for this Question:
Each exterior angle of a regular polygon:
$$\frac{360^\circ}{n}$$
Concept Behind This Question:
Students should calculate the exterior angle of a regular polygon.
Step-by-Step Solution:
For a regular hexagon,
$$n=6$$
$$\frac{360^\circ}{6}$$
$$=60^\circ$$
Therefore, the correct answer is:
$$60^\circ$$
Exam Tip:
This formula works only for regular polygons.
Q5. Which quadrilateral has diagonals that bisect each other at right angles?
A) Rectangle
B) Rhombus
C) Trapezium
D) Kite
Answer:
$$\text{Rhombus}$$
Useful Formula for this Question:
In a rhombus:
- Diagonals bisect each other.
- They intersect at $$90^\circ$$.
Concept Behind This Question:
Students should know the diagonal properties of special quadrilaterals.
Step-by-Step Solution:
The diagonals of a rhombus:
- Bisect each other.
- Meet at right angles.
Therefore, the correct answer is:
$$\text{Rhombus}$$
Exam Tip:
Remember that a square also has this property because it is a special rhombus.
Important Formulas & Concepts
1. Sum of Interior Angles of a Polygon
$$ (n-2)\times180^\circ $$
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 Rhombus
- All sides are equal.
- Opposite angles are equal.
- Diagonals bisect each other at right angles.
6. Properties of a Trapezium
- Exactly one pair of opposite sides is parallel.
FAQs
1. How many diagonals does a hexagon have?
$$9$$
2. What is the angle sum of an octagon?
$$1080^\circ$$
3. Which quadrilateral has all sides equal?
A rhombus and a square.
4. What is the exterior angle of a regular hexagon?
$$60^\circ$$
5. Which quadrilateral has diagonals meeting at right angles?
A rhombus.
Common Mistakes
❌ Using the wrong polygon angle formula.
❌ Confusing a rhombus with a rectangle.
❌ Forgetting that exterior angles always sum to $$360^\circ$$.
❌ Calculating diagonals incorrectly.
❌ Mixing the properties of a kite and a rhombus.
Quick Revision Notes
✔ Hexagon has $$9$$ diagonals.
✔ Octagon angle sum is $$1080^\circ$$.
✔ Exterior angle of a regular polygon:
$$\frac{360^\circ}{n}$$
✔ Rhombus has four equal sides.
✔ Rhombus diagonals bisect each other at right angles.
✔ Exterior angles of every polygon add up to $$360^\circ$$.
Conclusion
Understanding Quadrilaterals is an important chapter in Class 8 Mathematics. A clear understanding of polygons, quadrilaterals, diagonals, and angle properties helps students solve geometry problems accurately. Regular MCQ practice strengthens conceptual understanding, improves confidence, and enhances examination performance.
Related links
- 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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