GJK is an equilateral triangle, ABCD is a rectangle and JKEF is a trapezium. GJF and GKE are straight lines. If ∠r = 69°, find

1. ∠JFE
2. Sum of ∠m, ∠n, ∠p and ∠q.

(a)
∠GJK = 60° (Equilateral triangle)

∠JFE = ∠GJK = 60° (Corresponding angles)

(b)
∠ABC = 90° (Right angle)

∠BAD = 90° (Right angle)

∠s + ∠t 
= 180° - 90°
= 90° (Angles sum of triangle)

∠u + ∠v
= 180° - 90°
= 90° (Angles sum of triangle)

∠m + ∠r + ∠s = 180° (Angles on a straight line)

∠n + ∠t = 180° (Angles on a straight line)

∠p + ∠u = 180° (Angles on a straight line)

∠q + ∠v = 180° (Angles on a straight line)

Sum of ∠m, ∠n, ∠p, ∠q and ∠r
= (∠m + ∠n + ∠p + ∠q + ∠r + ∠s + ∠t + ∠u + ∠v) - (∠s + ∠t  + ∠u + ∠v)
= (4 x 180°) - (2 x 90°)
= 720° - 180°
= 540°

Sum of ∠m, ∠n, ∠p and ∠q
= 540° - 69° 
= 471°

Answer(s): (a) 60°; (b) 471°