The figure, not drawn to scale, is made up of an isosceles triangle and a rhombus. ∠k = ∠m, ∠i is thrice ∠m, ∠j is twice ∠n and ∠k is less than ∠n by 30°.
- Find ∠k.
- Find the difference between ∠i and ∠k.
(a)
∠k = 1 u
∠m = 1 u
∠n = 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°
∠k = 1 u = 40°
(b)
∠i = 3 u
∠i - ∠k
= 3 u - 1 u
= 2 u
= 2 x 40°
= 80°
Answer(s): (a) 40°; (b) 80°