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