# Exercise 6.3

QUESTION 1

Find the value of the unknown ** x** in the following diagrams :

The sum of all interior angles of a triangle is 180°. By using this property, these problems can be

solved as follows.

(i) x + 50° + 60° = 180°

x + 110° = 180°

x = 180° -110°

x = 70°

(ii) x + 90° + 30° = 180°

x + 120° = 180°

x = 180° – 120°

x = 60°

(iii) x + 30° + 110° = 180°

x + 140° = 180°

x = 180° – 140°

x = 40°

(iv) 50° + x + x = 180°

50° + 2x = 180°

2x = 180° – 50°

(v) x + x + x = 180°

3x = 180° – 90°

QUESTION 2

**Find the value of the unknowns x and y in the following diagrams:**

Sol :

(i) y+ 120° = 180° (Linear pair)

y = 180° – 120°

y = 60°

x + y + 50° = 180° (Angle sum property)

x + 60° + 50° = 180°

x + 110° = 180°

x = 180° – 10°

x = 70°

(ii) y = 80° (Vertically opposite angles)

y + x + 50° = 180° (Angle sum property)

80° + x + 50° =180°

x + 130° = 180°

x = 180° – 130°

x = 50°

(iii) y + 50° + 60° = 180° (Angle sum property)

y = 180° – 60° – 50°

y = 70°

x + y = 180° (Linear pair)

x = 180° – y

x = 180°-70°

x = 110°

(iv) x = 60° (Vertically opposite angles)

30° + x + y = 180°

30° + 60° + y = 180°

y = 180° – 30° – 60°

y = 90°

(v) y = 90° (Vertically opposite angles)

x + x + y = 180° (Angle sum property)

2x + y = 180°

2x + 90° = 180°

2x = 180° – 90°

(vi)

y = x ( Vertically opposite angles )

a = x ( Vertically opposite angles )

b = x ( Vertically opposite angles )

a + b+ y=180° (Angle sum property)

x + x + x = 180°

3x = 180°

y = x = 60°