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