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 = 41°, ∠LMK = 34° and ∠GKH = 114°, find
- ∠x
- ∠z
- ∠y
(a)
∠LKM = ∠GKH = 114° (Vertically opposite angles)
∠x
= 180° - 114° - 34°
= 32° (Angles sum of triangle)
(b)
∠z
= 180° - 32°
= 148° (Interior angles)
(c)
∠y
= 180° - 32° - 32° - 34°
= 105° (Angles sum of triangle)
Answer(s): (a) 32°; (b) 148°; (c) 105°