The figure, not drawn to scale, is made up of an isosceles triangle and a rhombus. ∠c = ∠d, ∠a is thrice ∠d, ∠b is thrice ∠e and ∠c is less than ∠e by 33°.
- Find ∠c.
- Find the difference between ∠a and ∠c.
(a)
∠c = 1 u
∠d = 1 u
∠e = 1 u + 33°
1 u + 33° + 1 u + 33° + 1 u = 180° (Angles sum of triangle)
3 u + 66° = 180°
3 u = 180° - 66° = 114°
1 u = 114° ÷ 3 = 38°
∠c = 1 u = 38°
(b)
∠a = 3 u
∠a - ∠c
= 3 u - 1 u
= 2 u
= 2 x 38°
= 76°
Answer(s): (a) 38°; (b) 76°