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