LNP is an equilateral triangle, EFGH is a rectangle and NPJK is a trapezium. LNK and LPJ are straight lines. If ∠v = 68°, find
- ∠NKJ
- Sum of ∠r, ∠s, ∠t and ∠u.
(a)
∠LNP = 60° (Equilateral triangle)
∠NKJ = ∠LNP = 60° (Corresponding angles)
(b)
∠EFG = 90° (Right angle)
∠FEH = 90° (Right angle)
∠w + ∠x
= 180° - 90°
= 90° (Angles sum of triangle)
∠y + ∠z
= 180° - 90°
= 90° (Angles sum of triangle)
∠r + ∠v + ∠w = 180° (Angles on a straight line)
∠s + ∠x = 180° (Angles on a straight line)
∠t + ∠y = 180° (Angles on a straight line)
∠u + ∠z = 180° (Angles on a straight line)
Sum of ∠r, ∠s, ∠t, ∠u and ∠v
= (∠r + ∠s + ∠t + ∠u + ∠v + ∠w + ∠x + ∠y + ∠z) - (∠w + ∠x + ∠y + ∠z)
= (4 x 180°) - (2 x 90°)
= 720° - 180°
= 540°
Sum of ∠r, ∠s, ∠t and ∠u
= 540° - 68°
= 472°
Answer(s): (a) 60°; (b) 472°