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