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