JLM is an equilateral triangle, CDEF is a rectangle and LMGH is a trapezium. JLH and JMG are straight lines. If ∠t = 84°, find

1. ∠LHG
2. Sum of ∠p, ∠q, ∠r and ∠s.

(a)
∠JLM = 60° (Equilateral triangle)

∠LHG = ∠JLM = 60° (Corresponding angles)

(b)
∠CDE = 90° (Right angle)

∠DCF = 90° (Right angle)

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

∠w + ∠x
= 180° - 90°
= 90° (Angles sum of triangle)

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

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

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

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

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

Sum of ∠p, ∠q, ∠r and ∠s
= 540° - 84° 
= 456°

Answer(s): (a) 60°; (b) 456°