KMN is an equilateral triangle, DEFG is a rectangle and MNHJ is a trapezium. KMJ and KNH are straight lines. If ∠u = 79°, find

1. ∠MJH
2. Sum of ∠q, ∠r, ∠s and ∠t.

(a)
∠KMN = 60° (Equilateral triangle)

∠MJH = ∠KMN = 60° (Corresponding angles)

(b)
∠DEF = 90° (Right angle)

∠EDG = 90° (Right angle)

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

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

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

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

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

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

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

Sum of ∠q, ∠r, ∠s and ∠t
= 540° - 79° 
= 461°

Answer(s): (a) 60°; (b) 461°