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