The figure, not drawn to scale, is made up of an isosceles triangle and a rhombus. ∠y = ∠z, ∠w is twice ∠z, ∠x is thrice ∠a and ∠y is less than ∠a by 30°.
- Find ∠y.
- Find the difference between ∠w and ∠y.
(a)
∠y = 1 u
∠z = 1 u
∠a = 1 u + 30°
1 u + 30° + 1 u + 30° + 1 u = 180° (Angles sum of triangle)
3 u + 60° = 180°
3 u = 180° - 60° = 120°
1 u = 120° ÷ 3 = 40°
∠y = 1 u = 40°
(b)
∠w = 2 u
∠w - ∠y
= 2 u - 1 u
= 1 u
= 1 x 40°
= 40°
Answer(s): (a) 40°; (b) 40°