The figure, not drawn to scale, is made up of an isosceles triangle and a rhombus. ∠g = ∠h, ∠e is thrice ∠h, ∠f is thrice ∠i and ∠g is less than ∠i by 36°.
- Find ∠g.
- Find the difference between ∠e and ∠g.
(a)
∠g = 1 u
∠h = 1 u
∠i = 1 u + 36°
1 u + 36° + 1 u + 36° + 1 u = 180° (Angles sum of triangle)
3 u + 72° = 180°
3 u = 180° - 72° = 108°
1 u = 108° ÷ 3 = 36°
∠g = 1 u = 36°
(b)
∠e = 3 u
∠e - ∠g
= 3 u - 1 u
= 2 u
= 2 x 36°
= 72°
Answer(s): (a) 36°; (b) 72°