Updated By SaraNextGen

On March 11, 2024, 11:35 AM

Question 1:

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

Answer:

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° = 70°

(ii) x + 90° + 30° = 180°

x + 120° = 180°

x = 180° − 120° = 60°

(iii) x + 30° + 110° = 180°

x + 140° = 180°

x = 180° − 140° = 40°

(iv) 50° + x + x = 180°

50° + 2x = 180°

2x = 180° − 50° = 130°

(v) x + x + x = 180°

3x = 180°

(vi) x + 2x + 90° = 180°

3x = 180° − 90° = 90º

Question 2:

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

Answer:

(i) y + 120° = 180° (Linear pair)

y = 180° − 120º = 60º

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

x + 60° + 50° = 180°

x + 110° = 180°

x = 180° − 110° = 70°

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

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

80° + x + 50° = 180°

x + 130º = 180°

x = 180° − 130º = 50°

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

y = 180° − 60° − 50° = 70°

x + y = 180° (Linear pair)

x = 180° − y = 180° − 70° = 110°

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

30° + x + y = 180°

30° + 60° + y = 180°

y = 180° − 30° − 60° = 90°

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

x + x + y = 180° (Angle sum property)

2x + y = 180°

2x + 90° = 180°

2x = 180° − 90° = 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°