Question

Find the values of a and b.

a
The diagram is not drawn to scale.
a =
U
b =
U

Answer 1

a = 36°

b = 144°

Explanation:

Method 1

Number of sides = n = 10

Sum of interior angles = (n - 2) × 180°

= (10 - 2) × 180°

= 8 × 180°

= 1440°

Interior angle = b = sum of interior angles ÷ number of sides

b = 1440 ÷ 10

b = 144°

a + b = 180° (Sum of angles in the straight line)

a + 144° = 180°

a + 144° - 144° = 180° - 144°

a = 36°

Method 2

Number of sides = 10

Exterior angle = a = 360° ÷ Number of sides

a = 360° ÷ 10

a = 36°

a + b = 180° (Sum of angles in the straight line)

36° + b = 180°

36° + b - 36° = 180° - 36°

b = 144°