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