In the figure, FGH is parallel to LMN and the line LH cuts ∠GLN into half. Given that HL and GM are straight lines, ∠FGL = 43°, ∠LMK = 40° and ∠GKH = 120°, find
- ∠k
- ∠n
- ∠m
(a)
∠LKM = ∠GKH = 120° (Vertically opposite angles)
∠k
= 180° - 120° - 40°
= 20° (Angles sum of triangle)
(b)
∠n
= 180° - 20°
= 160° (Interior angles)
(c)
∠m
= 180° - 20° - 20° - 40°
= 97° (Angles sum of triangle)
Answer(s): (a) 20°; (b) 160°; (c) 97°