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 = 46°, ∠LMK = 37° and ∠GKH = 112°, find
- ∠k
- ∠n
- ∠m
(a)
∠LKM = ∠GKH = 112° (Vertically opposite angles)
∠k
= 180° - 112° - 37°
= 31° (Angles sum of triangle)
(b)
∠n
= 180° - 31°
= 149° (Interior angles)
(c)
∠m
= 180° - 31° - 31° - 37°
= 97° (Angles sum of triangle)
Answer(s): (a) 31°; (b) 149°; (c) 97°