The figure, not drawn to scale, is made up of an isosceles triangle and a rhombus. ∠z = ∠a, ∠x is thrice ∠a, ∠y is twice ∠b and ∠z is less than ∠b by 30°.
- Find ∠z.
- Find the difference between ∠x and ∠z.
(a)
∠z = 1 u
∠a = 1 u
∠b = 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°
∠z = 1 u = 40°
(b)
∠x = 3 u
∠x - ∠z
= 3 u - 1 u
= 2 u
= 2 x 40°
= 80°
Answer(s): (a) 40°; (b) 80°