The figure, not drawn to scale, is made up of an isosceles triangle and a rhombus. ∠w = ∠x, ∠t is thrice ∠x, ∠v is twice ∠y and ∠w is less than ∠y by 33°.
- Find ∠w.
- Find the difference between ∠t and ∠w.
(a)
∠w = 1 u
∠x = 1 u
∠y = 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°
∠w = 1 u = 38°
(b)
∠t = 3 u
∠t - ∠w
= 3 u - 1 u
= 2 u
= 2 x 38°
= 76°
Answer(s): (a) 38°; (b) 76°