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Practice Class 8 Maths Chapter 3 Understanding Quadrilaterals MCQ Questions with Answers based on NCERT syllabus. Learn polygons, quadrilaterals, interior and exterior angles, diagonals, regular polygons, 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 in Class 8 Mathematics that develops students’ knowledge of polygons, quadrilaterals, angle properties, and diagonals. A strong understanding of these concepts helps in solving geometry questions accurately.
What You Will Learn?
✔ Polygons
✔ Quadrilaterals
✔ Interior Angle Sum Property
✔ Exterior Angle Property
✔ Regular Polygons
✔ Diagonals
✔ Parallelogram
✔ Rectangle, Square, Rhombus, and Trapezium
Why This Topic Is Important?
The concepts of quadrilaterals are useful in engineering, architecture, map-making, construction, and computer graphics. Understanding these properties improves logical reasoning and geometry 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. A regular polygon has each exterior angle equal to $$24^\circ$$. How many sides does it have?
A) $$12$$
B) $$15$$
C) $$16$$
D) $$18$$
Answer:
$$15$$
Useful Formula for this Question:
$$n=\frac{360^\circ}{\text{Exterior Angle}}$$
Concept Behind This Question:
Students should determine the number of sides of a regular polygon.
Step-by-Step Solution:
Given:
$$\text{Exterior Angle}=24^\circ$$
Therefore,
$$n=\frac{360}{24}=15$$
Hence, the polygon has:
$$15$$ sides.
Therefore, the correct answer is:
$$15$$
Exam Tip:
Always divide $$360^\circ$$ by the exterior angle.
Q2. Which quadrilateral always has diagonals that are perpendicular bisectors of each other?
A) Rectangle
B) Rhombus
C) Trapezium
D) Kite
Answer:
$$\text{Rhombus}$$
Useful Formula for this Question:
In a rhombus:
- Diagonals bisect each other.
- Diagonals intersect at $$90^\circ$$.
Concept Behind This Question:
Students should understand the diagonal properties of a rhombus.
Step-by-Step Solution:
A rhombus has diagonals that bisect each other at right angles.
Therefore, the correct answer is:
$$\text{Rhombus}$$
Exam Tip:
A square also has this property because it is a special rhombus.
Q3. Find the sum of the interior angles of a 12-sided polygon.
A) $$1620^\circ$$
B) $$1800^\circ$$
C) $$1980^\circ$$
D) $$2160^\circ$$
Answer:
$$1800^\circ$$
Useful Formula for this Question:
$$ (n-2)\times180^\circ $$
Concept Behind This Question:
Students should use the interior angle sum formula correctly.
Step-by-Step Solution:
For a 12-sided polygon,
$$n=12$$
$$=(12-2)\times180^\circ$$
$$=10\times180^\circ$$
$$=1800^\circ$$
Therefore, the correct answer is:
$$1800^\circ$$
Exam Tip:
Subtract $$2$$ from the number of sides before multiplying by $$180^\circ$$.
Q4. Which of the following is not a parallelogram?
A) Rectangle
B) Square
C) Rhombus
D) Trapezium
Answer:
$$\text{Trapezium}$$
Useful Formula for this Question:
A parallelogram has two pairs of opposite sides parallel.
Concept Behind This Question:
Students should identify quadrilaterals based on their properties.
Step-by-Step Solution:
Rectangle, square, and rhombus all have two pairs of opposite sides parallel.
A trapezium has only one pair of parallel sides.
Therefore, the correct answer is:
$$\text{Trapezium}$$
Exam Tip:
Every rectangle, rhombus, and square is a parallelogram.
Q5. How many diagonals does a 12-sided polygon have?
A) $$48$$
B) $$50$$
C) $$54$$
D) $$60$$
Answer:
$$54$$
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 12-sided polygon,
$$n=12$$
$$\frac{12(12-3)}{2}$$
$$=\frac{12\times9}{2}$$
$$=54$$
Therefore, the correct answer is:
$$54$$
Exam Tip:
Apply the diagonal formula carefully to avoid calculation mistakes.
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 Rhombus
- Four equal sides.
- Opposite angles are equal.
- Diagonals bisect each other at right angles.
6. Properties of a Square
- Four equal sides.
- Four right angles.
- Equal diagonals that bisect each other.
FAQs
1. How do you find the number of sides of a regular polygon?
Use:
$$n=\frac{360^\circ}{\text{Exterior Angle}}$$
2. Which quadrilateral has diagonals perpendicular to each other?
A rhombus and a square.
3. What is the interior angle sum of a 12-sided polygon?
$$1800^\circ$$
4. Which quadrilateral is not a parallelogram?
A trapezium.
5. How many diagonals does a 12-sided polygon have?
$$54$$
Common Mistakes
❌ Confusing a rhombus with a rectangle.
❌ Forgetting the diagonal formula.
❌ Incorrect calculation of polygon angle sums.
❌ Assuming every quadrilateral is a parallelogram.
❌ Using the wrong value of $$n$$.
Quick Revision Notes
✔ Exterior angle sum is always $$360^\circ$$.
✔ Rhombus diagonals bisect each other at right angles.
✔ Trapezium has only one pair of parallel sides.
✔ Interior angle sum formula:
$$ (n-2)\times180^\circ $$
✔ Number of diagonals:
$$\frac{n(n-3)}{2}$$
✔ Rectangle, square, and rhombus are all parallelograms.
Conclusion
Understanding Quadrilaterals is an essential chapter in Class 8 Mathematics. A thorough understanding of polygons, quadrilaterals, angle properties, and diagonals enables students to solve geometry problems confidently. Regular MCQ practice improves speed, accuracy, and conceptual understanding.
Related links
- 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 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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