The figure, not drawn to scale, is made up of an isosceles triangle and a rhombus. ∠s = ∠t, ∠q is twice ∠t, ∠r is twice ∠v and ∠s is less than ∠v by 33°.
- Find ∠s.
- Find the difference between ∠q and ∠s.
(a)
∠s = 1 u
∠t = 1 u
∠v = 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°
∠s = 1 u = 38°
(b)
∠q = 2 u
∠q - ∠s
= 2 u - 1 u
= 1 u
= 1 x 38°
= 38°
Answer(s): (a) 38°; (b) 38°