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Practice Class 8 Maths Chapter 3 Understanding Quadrilaterals MCQ Questions with Answers based on the NCERT latest syllabus. Solve difficult HOTS and concept-based MCQs on polygons, quadrilaterals, diagonals, angle properties, and regular polygons 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: Difficult (HOTS)
Based On: NCERT Latest Syllabus
Introduction:
This HOTS practice set contains advanced concept-based questions that require logical reasoning and the application of multiple formulas. These questions help students prepare for school examinations, Olympiads, and scholarship tests.
What You Will Learn?
✔ Interior Angle Applications
✔ Exterior Angle Applications
✔ Polygon Identification
✔ Number of Diagonals
✔ Properties of Special Quadrilaterals
✔ Multi-Step Geometry Problems
✔ Higher Order Thinking Skills (HOTS)
Why This Topic Is Important?
Understanding quadrilaterals and polygons is essential for higher geometry. Application-based questions strengthen mathematical reasoning and improve problem-solving speed.
Exam Relevance
These questions are useful for:
✔ CBSE Exams
✔ State Board Exams
✔ Olympiad Preparation
✔ Scholarship Exams
✔ Unit Tests
✔ Annual Examinations
Q1. A regular polygon has each interior angle equal to $$156^\circ$$. How many sides does it have?
A) $$12$$
B) $$15$$
C) $$18$$
D) $$20$$
Answer:
$$15$$
Useful Formula for this Question:
$$\frac{(n-2)\times180^\circ}{n}=\text{Interior Angle}$$
Concept Behind This Question:
Students should determine the number of sides from the interior angle of a regular polygon.
Step-by-Step Solution:
Given,
$$\frac{(n-2)\times180}{n}=156$$
$$180n-360=156n$$
$$24n=360$$
$$n=15$$
Therefore, the correct answer is:
$$15$$
Exam Tip:
Interior-angle questions usually require solving a simple equation.
Q2. A polygon has $$65$$ diagonals. The number of sides of the polygon is:
A) $$11$$
B) $$12$$
C) $$13$$
D) $$14$$
Answer:
$$13$$
Useful Formula for this Question:
$$D=\frac{n(n-3)}{2}$$
Concept Behind This Question:
Students should find the number of sides using the diagonal formula.
Step-by-Step Solution:
$$\frac{n(n-3)}{2}=65$$
$$n(n-3)=130$$
$$n^2-3n-130=0$$
$$(n-13)(n+10)=0$$
$$n=13$$
Therefore, the correct answer is:
$$13$$
Exam Tip:
Always reject the negative value while solving the quadratic equation.
Q3. Each exterior angle of a regular polygon is $$7.5^\circ$$. The number of sides is:
A) $$36$$
B) $$42$$
C) $$48$$
D) $$54$$
Answer:
$$48$$
Useful Formula for this Question:
$$\text{Exterior Angle}=\frac{360^\circ}{n}$$
Concept Behind This Question:
Students should determine the number of sides from the exterior angle.
Step-by-Step Solution:
$$n=\frac{360}{7.5}$$
$$=48$$
Therefore, the correct answer is:
$$48$$
Exam Tip:
When the exterior angle is a decimal, divide carefully.
Q4. Which quadrilateral always has diagonals that bisect each other but are not necessarily perpendicular or equal?
A) Rectangle
B) Rhombus
C) Parallelogram
D) Kite
Answer:
$$\text{Parallelogram}$$
Useful Formula for this Question:
In a parallelogram,
- Diagonals bisect each other.
Concept Behind This Question:
Students should compare the diagonal properties of different quadrilaterals.
Step-by-Step Solution:
A parallelogram always has diagonals that bisect each other.
However,
- They are not always equal.
- They are not always perpendicular.
Therefore, the correct answer is:
$$\text{Parallelogram}$$
Exam Tip:
A rectangle has equal diagonals, while a rhombus has perpendicular diagonals.
Q5. The sum of the interior angles of a polygon is $$1980^\circ$$. How many diagonals does the polygon have?
A) $$77$$
B) $$90$$
C) $$104$$
D) $$119$$
Answer:
$$77$$
Useful Formula for this Question:
Interior angle sum:
$$S=(n-2)\times180^\circ$$
Number of diagonals:
$$D=\frac{n(n-3)}{2}$$
Concept Behind This Question:
Students should combine two polygon formulas in one problem.
Step-by-Step Solution:
Given,
$$1980=(n-2)\times180$$
$$n-2=11$$
$$n=13$$
Now,
$$D=\frac{13(13-3)}{2}$$
$$=\frac{13\times10}{2}$$
$$=65$$
Therefore, the mathematically correct answer is:
$$65$$
Note: The options contain a typo. The correct option should be 65.
Exam Tip:
Always verify your final answer with the formula, even if it is not listed in the options.
Important Formulas & Concepts
1. Sum of Interior Angles
$$ (n-2)\times180^\circ $$
2. Sum of Exterior Angles
$$360^\circ$$
3. Interior Angle of a Regular Polygon
$$\frac{(n-2)\times180^\circ}{n}$$
4. Exterior Angle of a Regular Polygon
$$\frac{360^\circ}{n}$$
5. Number of Diagonals
$$\frac{n(n-3)}{2}$$
6. Properties of a Parallelogram
- Opposite sides are parallel.
- Opposite sides are equal.
- Opposite angles are equal.
- Diagonals bisect each other.
FAQs
1. Which polygon has $$65$$ diagonals?
A $$13$$-sided polygon.
2. What is the sum of the exterior angles of a convex polygon?
$$360^\circ$$
3. Which quadrilateral has diagonals that only bisect each other?
A parallelogram.
4. What is the interior angle of a regular 15-sided polygon?
$$156^\circ$$
5. Which formula is used to find the number of diagonals?
$$\frac{n(n-3)}{2}$$
Common Mistakes
❌ Forgetting to solve for the number of sides first.
❌ Mixing interior and exterior angle formulas.
❌ Assuming every parallelogram has equal diagonals.
❌ Ignoring decimal calculations.
❌ Making mistakes while solving quadratic equations.
Quick Revision Notes
✔ Interior angle sum:
$$ (n-2)\times180^\circ $$
✔ Exterior angle sum:
$$360^\circ$$
✔ Interior angle of a regular polygon:
$$\frac{(n-2)\times180^\circ}{n}$$
✔ Exterior angle:
$$\frac{360^\circ}{n}$$
✔ Number of diagonals:
$$\frac{n(n-3)}{2}$$
✔ A parallelogram has diagonals that bisect each other.
Conclusion
This HOTS practice set develops higher-level reasoning by combining multiple polygon concepts into single questions. Regular practice of such advanced MCQs improves conceptual clarity, calculation speed, and confidence for CBSE examinations, Olympiads, and scholarship tests.
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