The figure, not drawn to scale, is made up of an isosceles triangle and a rhombus. ∠e = ∠f, ∠c is thrice ∠f, ∠d is twice ∠g and ∠e is less than ∠g by 27°.
- Find ∠e.
- Find the difference between ∠c and ∠e.
(a)
∠e = 1 u
∠f = 1 u
∠g = 1 u + 27°
1 u + 27° + 1 u + 27° + 1 u = 180° (Angles sum of triangle)
3 u + 54° = 180°
3 u = 180° - 54° = 126°
1 u = 126° ÷ 3 = 42°
∠e = 1 u = 42°
(b)
∠c = 3 u
∠c - ∠e
= 3 u - 1 u
= 2 u
= 2 x 42°
= 84°
Answer(s): (a) 42°; (b) 84°