The figure, not drawn to scale, is made up of an isosceles triangle and a rhombus. ∠t = ∠v, ∠r is thrice ∠v, ∠s is twice ∠w and ∠t is less than ∠w by 27°.
- Find ∠t.
- Find the difference between ∠r and ∠t.
(a)
∠t = 1 u
∠v = 1 u
∠w = 1 u + 27°
1 u + 27° + 1 u + 27° + 1 u = 180° (Angles sum of triangle)
3 u + 54° = 180°
3 u = 180° - 54° = 126°
1 u = 126° ÷ 3 = 42°
∠t = 1 u = 42°
(b)
∠r = 3 u
∠r - ∠t
= 3 u - 1 u
= 2 u
= 2 x 42°
= 84°
Answer(s): (a) 42°; (b) 84°