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