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Practice Class 8 Maths Chapter 3 Understanding Quadrilaterals MCQ Questions with Answers based on the NCERT latest syllabus. Solve advanced HOTS MCQs on polygons, quadrilaterals, diagonals, interior angles, exterior angles, and special quadrilaterals with detailed step-by-step 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 final advanced practice set contains challenging questions based on multiple concepts of polygons and quadrilaterals. Students need to apply formulas, logical reasoning, and conceptual understanding together to solve these HOTS questions accurately.
What You Will Learn?
✔ Advanced Polygon Applications
✔ Interior & Exterior Angle Problems
✔ Multi-Step Diagonal Questions
✔ Properties of Special Quadrilaterals
✔ Regular Polygon Concepts
✔ Higher Order Thinking Skills (HOTS)
✔ Exam-Oriented Problem Solving
Why This Topic Is Important?
Advanced geometry questions improve logical thinking and analytical skills. They are highly useful for scoring well in school examinations, scholarship tests, and Olympiads.
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 exterior angle equal to $$18^\circ$$. How many diagonals does it have?
A) $$135$$
B) $$152$$
C) $$170$$
D) $$189$$
Answer:
$$170$$
Useful Formula for this Question:
$$n=\frac{360^\circ}{\text{Exterior Angle}}$$
$$D=\frac{n(n-3)}{2}$$
Concept Behind This Question:
Students should first determine the number of sides and then calculate the number of diagonals.
Step-by-Step Solution:
Given,
$$\text{Exterior Angle}=18^\circ$$
$$n=\frac{360}{18}=20$$
Now,
$$D=\frac{20(20-3)}{2}$$
$$=\frac{20\times17}{2}$$
$$=170$$
Therefore, the correct answer is:
$$170$$
Exam Tip:
When two formulas are required, solve them one by one to avoid mistakes.
Q2. The sum of the interior angles of a polygon is $$2880^\circ$$. The number of sides of the polygon is:
A) $$16$$
B) $$17$$
C) $$18$$
D) $$19$$
Answer:
$$18$$
Useful Formula for this Question:
$$\text{Sum of Interior Angles}=(n-2)\times180^\circ$$
Concept Behind This Question:
Students should determine the number of sides using the interior angle sum.
Step-by-Step Solution:
Given,
$$2880=(n-2)\times180$$
$$n-2=16$$
$$n=18$$
Therefore, the correct answer is:
$$18$$
Exam Tip:
Always divide the angle sum by $$180^\circ$$ first.
Q3. A polygon has $$152$$ diagonals. How many sides does it have?
A) $$18$$
B) $$19$$
C) $$20$$
D) $$21$$
Answer:
$$19$$
Useful Formula for this Question:
$$D=\frac{n(n-3)}{2}$$
Concept Behind This Question:
Students should solve the quadratic equation obtained from the diagonal formula.
Step-by-Step Solution:
Given,
$$\frac{n(n-3)}{2}=152$$
$$n(n-3)=304$$
$$n^2-3n-304=0$$
$$(n-19)(n+16)=0$$
$$n=19$$
Therefore, the correct answer is:
$$19$$
Exam Tip:
Reject the negative root because the number of sides cannot be negative.
Q4. Which of the following quadrilaterals always has diagonals that are equal, perpendicular, and bisect each other?
A) Rectangle
B) Rhombus
C) Square
D) Parallelogram
Answer:
$$\text{Square}$$
Useful Formula for this Question:
Properties of a square:
- Four equal sides.
- Four right angles.
- Equal diagonals.
- Perpendicular diagonals.
- Diagonals bisect each other.
Concept Behind This Question:
Students should compare the diagonal properties of different quadrilaterals.
Step-by-Step Solution:
Only a square satisfies all the given conditions simultaneously.
Therefore, the correct answer is:
$$\text{Square}$$
Exam Tip:
Remember:
- Rectangle → Equal diagonals only.
- Rhombus → Perpendicular diagonals only.
- Square → Equal and perpendicular diagonals.
Q5. A regular polygon has $$30$$ sides. What is the measure of each interior angle?
A) $$162^\circ$$
B) $$164^\circ$$
C) $$168^\circ$$
D) $$170^\circ$$
Answer:
$$168^\circ$$
Useful Formula for this Question:
$$\text{Interior Angle}=\frac{(n-2)\times180^\circ}{n}$$
Concept Behind This Question:
Students should calculate the interior angle of a regular polygon.
Step-by-Step Solution:
For
$$n=30$$
$$\frac{(30-2)\times180}{30}$$
$$=\frac{28\times180}{30}$$
$$=168^\circ$$
Therefore, the correct answer is:
$$168^\circ$$
Exam Tip:
As the number of sides increases, each interior angle approaches $$180^\circ$$.
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. Important Properties of Quadrilaterals
- Parallelogram: Opposite sides are parallel and equal; diagonals bisect each other.
- Rectangle: Equal diagonals that bisect each other.
- Rhombus: Perpendicular diagonals that bisect each other.
- Square: Equal and perpendicular diagonals that bisect each other.
- Trapezium: Exactly one pair of opposite sides is parallel.
FAQs
1. What is the sum of the exterior angles of any convex polygon?
$$360^\circ$$
2. Which polygon has $$152$$ diagonals?
A $$19$$-sided polygon.
3. Which quadrilateral has equal and perpendicular diagonals?
A square.
4. What is the interior angle of a regular $$30$$-sided polygon?
$$168^\circ$$
5. Which formula is used to find the number of diagonals?
$$\frac{n(n-3)}{2}$$
Common Mistakes
❌ Confusing interior angle and exterior angle formulas.
❌ Forgetting to determine the number of sides before calculating diagonals.
❌ Assuming rectangles have perpendicular diagonals.
❌ Ignoring simplification while solving quadratic equations.
❌ Mixing the properties of a rhombus and a square.
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 of a regular polygon:
$$\frac{360^\circ}{n}$$
✔ Number of diagonals:
$$\frac{n(n-3)}{2}$$
✔ Only a square has diagonals that are equal, perpendicular, and bisect each other.
Conclusion
This advanced HOTS practice set completes the study of Understanding Quadrilaterals by covering higher-level applications of polygon formulas and quadrilateral properties. Solving these challenging MCQs strengthens conceptual understanding, improves problem-solving speed, and prepares students for CBSE examinations, Olympiads, and scholarship tests.
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