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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 is an important chapter in Class 8 Mathematics that introduces students to the properties of polygons and different types of quadrilaterals. Mastering these concepts helps students solve geometry problems confidently and builds a strong foundation for higher mathematics.
What You Will Learn?
✔ Types of Polygons
✔ Quadrilaterals
✔ Interior Angle Sum Property
✔ Exterior Angle Property
✔ Number of Diagonals
✔ Regular Polygons
✔ Properties of Parallelogram, Rectangle, Rhombus, Square and Trapezium
Why This Topic Is Important?
Quadrilaterals are widely used in architecture, engineering, construction, surveying, and computer graphics. Understanding their properties improves logical reasoning and geometrical 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 interior angles of a 15-sided polygon is:
A) $$2160^\circ$$
B) $$2340^\circ$$
C) $$2520^\circ$$
D) $$2700^\circ$$
Answer:
$$2340^\circ$$
Useful Formula for this Question:
$$\text{Sum of Interior Angles}=(n-2)\times180^\circ$$
Concept Behind This Question:
Students should apply the interior angle sum formula correctly.
Step-by-Step Solution:
For a 15-sided polygon,
$$n=15$$
$$=(15-2)\times180^\circ$$
$$=13\times180^\circ$$
$$=2340^\circ$$
Therefore, the correct answer is:
$$2340^\circ$$
Exam Tip:
Always subtract $$2$$ from the number of sides before multiplying by $$180^\circ$$.
Q2. Which quadrilateral has diagonals that are equal, bisect each other, and meet at right angles?
A) Rectangle
B) Rhombus
C) Square
D) Trapezium
Answer:
$$\text{Square}$$
Useful Formula for this Question:
Properties of a square:
- Four equal sides.
- Four right angles.
- Equal diagonals.
- Diagonals bisect each other at $$90^\circ$$.
Concept Behind This Question:
Students should identify the unique properties of a square.
Step-by-Step Solution:
Only a square satisfies all the given conditions.
Therefore, the correct answer is:
$$\text{Square}$$
Exam Tip:
A square combines the properties of both a rectangle and a rhombus.
Q3. A regular polygon has each exterior angle equal to $$20^\circ$$. How many sides does it have?
A) $$16$$
B) $$18$$
C) $$20$$
D) $$24$$
Answer:
$$18$$
Useful Formula for this Question:
$$n=\frac{360^\circ}{\text{Exterior Angle}}$$
Concept Behind This Question:
Students should calculate the number of sides of a regular polygon.
Step-by-Step Solution:
Given,
$$\text{Exterior Angle}=20^\circ$$
$$n=\frac{360}{20}$$
$$=18$$
Therefore, the polygon has:
$$18$$ sides.
Hence, the correct answer is:
$$18$$
Exam Tip:
The sum of all exterior angles of any polygon is always $$360^\circ$$.
Q4. Which statement is true for a rectangle?
A) All sides are equal.
B) Opposite sides are equal and parallel.
C) Only one pair of opposite sides is parallel.
D) Diagonals are perpendicular.
Answer:
Opposite sides are equal and parallel.
Useful Formula for this Question:
Properties of a rectangle:
- Opposite sides are equal.
- Opposite sides are parallel.
- All angles are $$90^\circ$$.
Concept Behind This Question:
Students should identify the basic properties of a rectangle.
Step-by-Step Solution:
A rectangle has opposite sides equal and parallel but not all sides are equal.
Therefore, the correct answer is:
Opposite sides are equal and parallel.
Exam Tip:
A square is a special rectangle with all four sides equal.
Q5. How many diagonals does a 15-sided polygon have?
A) $$80$$
B) $$85$$
C) $$90$$
D) $$95$$
Answer:
$$90$$
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 formula.
Step-by-Step Solution:
For a 15-sided polygon,
$$n=15$$
$$\frac{15(15-3)}{2}$$
$$=\frac{15\times12}{2}$$
$$=90$$
Therefore, the correct answer is:
$$90$$
Exam Tip:
Practice the diagonal formula regularly for faster calculations.
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 Rectangle
- Opposite sides are equal and parallel.
- Four right angles.
- Equal diagonals that bisect each other.
6. Properties of a Square
- Four equal sides.
- Four right angles.
- Equal diagonals.
- Diagonals bisect each other at right angles.
FAQs
1. What is the sum of the interior angles of a 15-sided polygon?
$$2340^\circ$$
2. How many diagonals does a 15-sided polygon have?
$$90$$
3. Which quadrilateral has equal diagonals meeting at right angles?
A square.
4. How do you calculate the exterior angle of a regular polygon?
Use:
$$\frac{360^\circ}{n}$$
5. What are the properties of a rectangle?
Opposite sides are equal and parallel, all angles are $$90^\circ$$, and diagonals are equal.
Common Mistakes
❌ Using the wrong value of $$n$$ in formulas.
❌ Confusing the properties of a square and a rectangle.
❌ Forgetting that exterior angles always sum to $$360^\circ$$.
❌ Miscalculating the number of diagonals.
❌ Assuming all quadrilaterals have equal diagonals.
Quick Revision Notes
✔ Interior angle sum formula:
$$ (n-2)\times180^\circ $$
✔ Exterior angles always total $$360^\circ$$.
✔ Number of diagonals:
$$\frac{n(n-3)}{2}$$
✔ Rectangle has equal diagonals.
✔ Square has equal sides and equal diagonals meeting at $$90^\circ$$.
✔ A regular polygon with an exterior angle of $$20^\circ$$ has $$18$$ sides.
Conclusion
Understanding Quadrilaterals is one of the most important geometry chapters in Class 8 Mathematics. A strong understanding of polygons, angle properties, diagonals, and special quadrilaterals helps students solve geometry questions accurately and perform well in school and competitive examinations.
Related links
- 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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