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 27°.
- Find ∠x.
- Find the difference between ∠v and ∠x.
(a)
∠x = 1 u
∠y = 1 u
∠z = 1 u + 27°
1 u + 27° + 1 u + 27° + 1 u = 180° (Angles sum of triangle)
3 u + 54° = 180°
3 u = 180° - 54° = 126°
1 u = 126° ÷ 3 = 42°
∠x = 1 u = 42°
(b)
∠v = 2 u
∠v - ∠x
= 2 u - 1 u
= 1 u
= 1 x 42°
= 42°
Answer(s): (a) 42°; (b) 42°