The figure, not drawn to scale, is made up of an isosceles triangle and a rhombus. ∠p = ∠q, ∠m is thrice ∠q, ∠n is thrice ∠r and ∠p is less than ∠r by 33°.
- Find ∠p.
- Find the difference between ∠m and ∠p.
(a)
∠p = 1 u
∠q = 1 u
∠r = 1 u + 33°
1 u + 33° + 1 u + 33° + 1 u = 180° (Angles sum of triangle)
3 u + 66° = 180°
3 u = 180° - 66° = 114°
1 u = 114° ÷ 3 = 38°
∠p = 1 u = 38°
(b)
∠m = 3 u
∠m - ∠p
= 3 u - 1 u
= 2 u
= 2 x 38°
= 76°
Answer(s): (a) 38°; (b) 76°