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