**Chapter 6 The Triangle and its Properties Exercise 6.2**

Question 1.

Find the value of the unknown exterior angle x in the following diagrams:

Solution:

(i) ∠x = 50° + 70° = 120° (Exterior angle is equal to sum of its interior opposite angles)

(ii) ∠x = 65°+ 45° = 110° (Exterior angle is equal to sum of its interior opposite angles)

(iii) ∠x = 30° + 40° = 70° (Exterior angle is equal to sum of its interior opposite angles)

(iv) ∠x = 60° + 60° = 120° (Exterior angle is equal to sum of its interior opposite angles)

(v) ∠x = 50° + 50° =100° (Exterior angle is equal to sum of its interior opposite angles)

(vi) ∠x = 30° + 60° = 90° (Exterior angle is equal to sum of its interior opposite angle)

Question 2.

Find the value of the unknown interior angle x in the following figures:

Solution:

(i) ∠x + 50° = 115° (Exterior angle of a triangle)

∴ ∠x = 115°- 50° = 65°

(ii) ∠x + 70° = 110° (Exterior angle of a triangle)

∴ ∠x = 110° – 70° = 40°

(iii) ∠ x + 90° = 125° (Exterior angle of a right triangle)

∴ ∠x = 125° – 90° = 35°

(iv) ∠x + 60° = 120° (Exterior angle of a triangle)

∴ ∠x = 120° – 60° = 60°

(v)∠ X + 30° = 80° (Exterior angle of a triangle)

∴ ∠x = 80° – 30° = 50°

(vi) ∠ x + 35° = 75° (Exterior angle of a triangle)

∴ ∠ x = 75° – 35° = 40°