Class 9 Maths Chapter 6 Lines and Angles – Exercise 6.4 NCERT Solutions

Introduction

Exercise 6.4 explores the exterior angle property of triangles. You’ll learn how to prove that the measure of an exterior angle is equal to the sum of the two interior opposite angles, and apply this property to find unknown angles.

Key Concept

• Exterior Angle Property:

$$$$Exterior angle=Sum of two interior opposite angles

$$$$

Solved Questions (Step by Step)

Q1. In a triangle, one exterior angle is 120° and one interior opposite angle is 45°. Find the other interior opposite angle.

Solution:

$${120}^{\circ }={45}^{\circ }+x⟹x={75}^{\circ }$$

Q2. In a triangle, one exterior angle is 100° and one interior opposite angle is 40°. Find the other interior opposite angle.

Solution:

$${100}^{\circ }={40}^{\circ }+x⟹x={60}^{\circ }$$

Q3. In a triangle, one exterior angle is 90° and one interior opposite angle is 30°. Find the other interior opposite angle.

Solution:

$${90}^{\circ }={30}^{\circ }+x⟹x={60}^{\circ }$$

Q4. In a triangle, one exterior angle is 110° and one interior opposite angle is 50°. Find the other interior opposite angle.

Solution:

$${110}^{\circ }={50}^{\circ }+x⟹x={60}^{\circ }$$

Q5. In a triangle, one exterior angle is 80° and one interior opposite angle is 35°. Find the other interior opposite angle.

Solution:

$${80}^{\circ }={35}^{\circ }+x⟹x={45}^{\circ }$$

Q6. In a triangle, one exterior angle is 95° and one interior opposite angle is 40°. Find the other interior opposite angle.

Solution:

$${95}^{\circ }={40}^{\circ }+x⟹x={55}^{\circ }$$

Q7. In a triangle, one exterior angle is 70° and one interior opposite angle is 25°. Find the other interior opposite angle.

Solution:

$${70}^{\circ }={25}^{\circ }+x⟹x={45}^{\circ }$$

Q8. In a triangle, one exterior angle is 85° and one interior opposite angle is 50°. Find the other interior opposite angle.

Solution:

$${85}^{\circ }={50}^{\circ }+x⟹x={35}^{\circ }$$

Q9. In a triangle, one exterior angle is 150° and one interior opposite angle is 70°. Find the other interior opposite angle.

Solution:

$${150}^{\circ }={70}^{\circ }+x⟹x={80}^{\circ }$$

Q10. In a triangle, one exterior angle is 120° and one interior opposite angle is 60°. Find the other interior opposite angle.

Solution:

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

Q11. In a triangle, one exterior angle is 75° and one interior opposite angle is 30°. Find the other interior opposite angle.

Solution:

$${75}^{\circ }={30}^{\circ }+x⟹x={45}^{\circ }$$

Q12. In a triangle, one exterior angle is 135° and one interior opposite angle is 65°. Find the other interior opposite angle.

Solution:

$${135}^{\circ }={65}^{\circ }+x⟹x={70}^{\circ }$$

Q13. In a triangle, one exterior angle is 105° and one interior opposite angle is 45°. Find the other interior opposite angle.

Solution:

$${105}^{\circ }={45}^{\circ }+x⟹x={60}^{\circ }$$

Q14. In a triangle, one exterior angle is 140° and one interior opposite angle is 50°. Find the other interior opposite angle.

Solution:

$${140}^{\circ }={50}^{\circ }+x⟹x={90}^{\circ }$$

Q15. In a triangle, one exterior angle is 160° and one interior opposite angle is 75°. Find the other interior opposite angle.

Solution:

$${160}^{\circ }={75}^{\circ }+x⟹x={85}^{\circ }$$

FAQs (10 for Exercise 6.4)

1. Q: What is an exterior angle of a triangle? A: An angle formed outside the triangle when one side is extended.

2. Q: What is the exterior angle property? A: Exterior angle = sum of two interior opposite angles.

3. Q: Can an exterior angle be less than both interior opposite angles? A: No, it is always greater than each interior opposite angle individually.

4. Q: What is the maximum value of an exterior angle? A: Less than 180°, since it forms a linear pair with an interior angle.

5. Q: What is the minimum value of an exterior angle? A: Greater than 0°, since angles are positive.

6. Q: How many exterior angles can a triangle have? A: Three, one at each vertex.

7. Q: What is the relation between an exterior angle and its adjacent interior angle? A: They form a linear pair and sum to 180°.

8. Q: Why is the exterior angle property important? A: It helps solve unknown angles in triangles.

9. Q: Can the exterior angle property be extended to polygons? A: Yes, exterior angles of polygons also relate to interior angles.

10. Q: What is the sum of all exterior angles of a polygon? A: 360°.

Conclusion

Exercise 6.4 has 15 questions that strengthen your understanding of the exterior angle property of triangles. This completes Chapter 6 of Class 9 Maths.

Visit:www.fuzymathacademy.com