The figure, not drawn to scale, is made up of an isosceles triangle and a rhombus. ∠x = ∠y, ∠v is twice ∠y, ∠w is thrice ∠z and ∠x is less than ∠z by 33°.
- Find ∠x.
- Find the difference between ∠v and ∠x.
(a)
∠x = 1 u
∠y = 1 u
∠z = 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°
∠x = 1 u = 38°
(b)
∠v = 2 u
∠v - ∠x
= 2 u - 1 u
= 1 u
= 1 x 38°
= 38°
Answer(s): (a) 38°; (b) 38°