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 30°.
- Find ∠r.
- Find the difference between ∠p and ∠r.
(a)
∠r = 1 u
∠s = 1 u
∠t = 1 u + 30°
1 u + 30° + 1 u + 30° + 1 u = 180° (Angles sum of triangle)
3 u + 60° = 180°
3 u = 180° - 60° = 120°
1 u = 120° ÷ 3 = 40°
∠r = 1 u = 40°
(b)
∠p = 3 u
∠p - ∠r
= 3 u - 1 u
= 2 u
= 2 x 40°
= 80°
Answer(s): (a) 40°; (b) 80°