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