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