The figure, not drawn to scale, is made up of an isosceles triangle and a rhombus. ∠b = ∠c, ∠z is twice ∠c, ∠a is twice ∠d and ∠b is less than ∠d by 27°.
- Find ∠b.
- Find the difference between ∠z and ∠b.
(a)
∠b = 1 u
∠c = 1 u
∠d = 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°
∠b = 1 u = 42°
(b)
∠z = 2 u
∠z - ∠b
= 2 u - 1 u
= 1 u
= 1 x 42°
= 42°
Answer(s): (a) 42°; (b) 42°