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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 sum property, 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 helps students understand the properties of polygons and special quadrilaterals. This chapter develops geometric reasoning and provides the foundation for advanced geometry.
What You Will Learn?
✔ Types of Polygons
✔ Interior and Exterior Angle Properties
✔ Regular Polygons
✔ Number of Diagonals
✔ Parallelogram
✔ Rectangle
✔ Rhombus
✔ Square and Trapezium
Why This Topic Is Important?
The concepts of quadrilaterals are widely used in architecture, engineering, surveying, and design. A good understanding of these concepts improves mathematical thinking and 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 an 11-sided polygon is:
A) $$1440^\circ$$
B) $$1620^\circ$$
C) $$1800^\circ$$
D) $$1980^\circ$$
Answer:
$$1620^\circ$$
Useful Formula for this Question:
$$\text{Sum of Interior Angles}=(n-2)\times180^\circ$$
Concept Behind This Question:
Students should apply the angle sum formula correctly.
Step-by-Step Solution:
For an 11-sided polygon,
$$n=11$$
$$=(11-2)\times180^\circ$$
$$=9\times180^\circ$$
$$=1620^\circ$$
Therefore, the correct answer is:
$$1620^\circ$$
Exam Tip:
Subtract $$2$$ from the number of sides before multiplying by $$180^\circ$$.
Q2. Which quadrilateral has diagonals that bisect each other but are not necessarily equal?
A) Rectangle
B) Parallelogram
C) Kite
D) Trapezium
Answer:
$$\text{Parallelogram}$$
Useful Formula for this Question:
Properties of a parallelogram:
- Opposite sides are parallel.
- Diagonals bisect each other.
Concept Behind This Question:
Students should identify the diagonal properties of a parallelogram.
Step-by-Step Solution:
In a parallelogram, the diagonals always bisect each other, but they are not always equal.
Therefore, the correct answer is:
$$\text{Parallelogram}$$
Exam Tip:
Equal diagonals are a property of rectangles and squares, not every parallelogram.
Q3. A regular polygon has each exterior angle equal to $$18^\circ$$. How many sides does it have?
A) $$18$$
B) $$20$$
C) $$22$$
D) $$24$$
Answer:
$$20$$
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:
$$n=\frac{360}{18}$$
$$=20$$
Therefore, the polygon has:
$$20$$ sides.
Hence, the correct answer is:
$$20$$
Exam Tip:
The number of sides is always obtained by dividing $$360^\circ$$ by the exterior angle.
Q4. How many diagonals does a 13-sided polygon have?
A) $$60$$
B) $$62$$
C) $$65$$
D) $$68$$
Answer:
$$65$$
Useful Formula for this Question:
$$\frac{n(n-3)}{2}$$
Concept Behind This Question:
Students should calculate diagonals using the standard formula.
Step-by-Step Solution:
For a 13-sided polygon,
$$n=13$$
$$\frac{13(13-3)}{2}$$
$$=\frac{13\times10}{2}$$
$$=65$$
Therefore, the correct answer is:
$$65$$
Exam Tip:
Remember the diagonal formula for all polygons.
Q5. Which statement is correct about a rectangle?
A) All sides are equal.
B) Opposite sides are equal and all angles are $$90^\circ$$.
C) Diagonals are perpendicular.
D) Only one pair of opposite sides is parallel.
Answer:
Opposite sides are equal and all angles are $$90^\circ$$.
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 always has opposite sides equal and parallel with four right angles.
Therefore, the correct answer is:
Opposite sides are equal and all angles are $$90^\circ$$.
Exam Tip:
A rectangle is a parallelogram with four right angles.
Important Formulas & Concepts
1. Sum of Interior Angles
$$ (n-2)\times180^\circ $$
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 Parallelogram
- Opposite sides are equal.
- Opposite sides are parallel.
- Opposite angles are equal.
- Diagonals bisect each other.
6. Properties of a Rectangle
- Four right angles.
- Equal opposite sides.
- Equal diagonals.
FAQs
1. What is the sum of the interior angles of an 11-sided polygon?
$$1620^\circ$$
2. How many diagonals does a 13-sided polygon have?
$$65$$
3. What is the exterior angle of a regular 20-sided polygon?
$$18^\circ$$
4. Which quadrilateral has diagonals that bisect each other?
A parallelogram.
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 $$n$$.
❌ Forgetting the diagonal formula.
❌ Confusing a rectangle with a rhombus.
❌ Assuming every parallelogram has equal diagonals.
❌ Incorrectly calculating polygon angles.
Quick Revision Notes
✔ Interior angle sum:
$$ (n-2)\times180^\circ $$
✔ Exterior angle sum:
$$360^\circ$$
✔ Number of diagonals:
$$\frac{n(n-3)}{2}$$
✔ Rectangle has four right angles.
✔ Parallelogram diagonals bisect each other.
✔ A regular 20-sided polygon has an exterior angle of $$18^\circ$$.
Conclusion
Understanding Quadrilaterals is an important chapter in Class 8 Mathematics. A strong understanding of polygons, angle properties, diagonals, and special quadrilaterals helps students solve geometry questions efficiently and score better in examinations.
Related links
- Class 8 Maths Chapter 3 Understanding Quadrilaterals part-9
- 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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