The figure, not drawn to scale, is made up of an isosceles triangle and a rhombus. ∠f = ∠g, ∠d is twice ∠g, ∠e is twice ∠h and ∠f is less than ∠h by 36°.
- Find ∠f.
- Find the difference between ∠d and ∠f.
(a)
∠f = 1 u
∠g = 1 u
∠h = 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°
∠f = 1 u = 36°
(b)
∠d = 2 u
∠d - ∠f
= 2 u - 1 u
= 1 u
= 1 x 36°
= 36°
Answer(s): (a) 36°; (b) 36°