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