Class 9 Maths Chapter 8 Quadrilaterals – Exercise 8.1 NCERT Solutions

Introduction

Exercise 8.1 introduces the angle sum property of quadrilaterals. You’ll learn how to prove that the sum of the angles of a quadrilateral is 360°, and apply this property to solve problems involving missing angles.

Key Concept

• Angle Sum Property of Quadrilaterals:

$$\mathrm{\angle }A+\mathrm{\angle }B+\mathrm{\angle }C+\mathrm{\angle }D={360}^{\circ }$$

• This follows from dividing a quadrilateral into two triangles.

Solved Questions (Step by Step)

Q1. In a quadrilateral, three angles are 90°, 85°, and 95°. Find the fourth angle.

Solution:

$${90}^{\circ }+{85}^{\circ }+{95}^{\circ }+x={360}^{\circ }⟹x={90}^{\circ }$$

Q2. In a quadrilateral, three angles are 100°, 80°, and 75°. Find the fourth angle.

Solution:

$${100}^{\circ }+{80}^{\circ }+{75}^{\circ }+x={360}^{\circ }⟹x={105}^{\circ }$$

Q3. In a quadrilateral, three angles are 120°, 110°, and 60°. Find the fourth angle.

Solution:

$${120}^{\circ }+{110}^{\circ }+{60}^{\circ }+x={360}^{\circ }⟹x={70}^{\circ }$$

Q4. In a quadrilateral, three angles are 90°, 90°, and 80°. Find the fourth angle.

Solution:

$${90}^{\circ }+{90}^{\circ }+{80}^{\circ }+x={360}^{\circ }⟹x={100}^{\circ }$$

Q5. In a quadrilateral, three angles are 95°, 85°, and 100°. Find the fourth angle.

Solution:

$${95}^{\circ }+{85}^{\circ }+{100}^{\circ }+x={360}^{\circ }⟹x={80}^{\circ }$$

Q6. In a quadrilateral, three angles are 70°, 110°, and 90°. Find the fourth angle.

Solution:

$${70}^{\circ }+{110}^{\circ }+{90}^{\circ }+x={360}^{\circ }⟹x={90}^{\circ }$$

Q7. In a quadrilateral, three angles are 85°, 95°, and 90°. Find the fourth angle.

Solution:

$${85}^{\circ }+{95}^{\circ }+{90}^{\circ }+x={360}^{\circ }⟹x={90}^{\circ }$$

Q8. In a quadrilateral, three angles are 100°, 120°, and 80°. Find the fourth angle.

Solution:

$${100}^{\circ }+{120}^{\circ }+{80}^{\circ }+x={360}^{\circ }⟹x={60}^{\circ }$$

Q9. In a quadrilateral, three angles are 75°, 85°, and 95°. Find the fourth angle.

Solution:

$${75}^{\circ }+{85}^{\circ }+{95}^{\circ }+x={360}^{\circ }⟹x={105}^{\circ }$$

Q10. In a quadrilateral, three angles are 110°, 100°, and 70°. Find the fourth angle.

Solution:

$${110}^{\circ }+{100}^{\circ }+{70}^{\circ }+x={360}^{\circ }⟹x={80}^{\circ }$$

Q11. In a quadrilateral, three angles are 120°, 90°, and 60°. Find the fourth angle.

Solution:

$${120}^{\circ }+{90}^{\circ }+{60}^{\circ }+x={360}^{\circ }⟹x={90}^{\circ }$$

Q12. In a quadrilateral, three angles are 130°, 80°, and 70°. Find the fourth angle.

Solution:

$${130}^{\circ }+{80}^{\circ }+{70}^{\circ }+x={360}^{\circ }⟹x={80}^{\circ }$$

Q13. In a quadrilateral, three angles are 140°, 100°, and 60°. Find the fourth angle.

Solution:

$${140}^{\circ }+{100}^{\circ }+{60}^{\circ }+x={360}^{\circ }⟹x={60}^{\circ }$$

Q14. In a quadrilateral, three angles are 150°, 90°, and 70°. Find the fourth angle.

Solution:

$${150}^{\circ }+{90}^{\circ }+{70}^{\circ }+x={360}^{\circ }⟹x={50}^{\circ }$$

Q15. In a quadrilateral, three angles are 80°, 85°, and 95°. Find the fourth angle.

Solution:

$${80}^{\circ }+{85}^{\circ }+{95}^{\circ }+x={360}^{\circ }⟹x={100}^{\circ }$$

FAQs (10 for Exercise 8.1)

1. Q: What is the angle sum property of quadrilaterals? A: The sum of all four angles is 360°.

2. Q: How do you prove the angle sum property? A: By dividing a quadrilateral into two triangles.

3. Q: Can a quadrilateral have all angles equal? A: Yes, in a square or rectangle (each 90°).

4. Q: What is a convex quadrilateral? A: A quadrilateral with all interior angles less than 180°.

5. Q: What is a concave quadrilateral? A: A quadrilateral with one interior angle greater than 180°.

6. Q: What is the sum of angles in a triangle? A: 180°.

7. Q: How many diagonals does a quadrilateral have? A: Two.

8. Q: What is a parallelogram? A: A quadrilateral with opposite sides parallel.

9. Q: What is a trapezium? A: A quadrilateral with one pair of parallel sides.

10. Q: Why is the angle sum property important? A: It helps solve missing angles and proves geometric facts.

Conclusion

Exercise 8.1 has 15 questions that strengthen your understanding of the angle sum property of quadrilaterals. This builds the foundation for studying special quadrilaterals like parallelograms, trapeziums, and rhombuses.

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