The figure, not drawn to scale, is made up of an isosceles triangle and a rhombus. ∠r = ∠s, ∠p is twice ∠s, ∠q is twice ∠t and ∠r is less than ∠t by 36°.
- Find ∠r.
- Find the difference between ∠p and ∠r.
(a)
∠r = 1 u
∠s = 1 u
∠t = 1 u + 36°
1 u + 36° + 1 u + 36° + 1 u = 180° (Angles sum of triangle)
3 u + 72° = 180°
3 u = 180° - 72° = 108°
1 u = 108° ÷ 3 = 36°
∠r = 1 u = 36°
(b)
∠p = 2 u
∠p - ∠r
= 2 u - 1 u
= 1 u
= 1 x 36°
= 36°
Answer(s): (a) 36°; (b) 36°