The figure, not drawn to scale, is made up of an isosceles triangle and a rhombus. ∠h = ∠i, ∠f is thrice ∠i, ∠g is thrice ∠j and ∠h is less than ∠j by 27°.
- Find ∠h.
- Find the difference between ∠f and ∠h.
(a)
∠h = 1 u
∠i = 1 u
∠j = 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°
∠h = 1 u = 42°
(b)
∠f = 3 u
∠f - ∠h
= 3 u - 1 u
= 2 u
= 2 x 42°
= 84°
Answer(s): (a) 42°; (b) 84°