In the figure, JKL is parallel to PQR and the line PL cuts ∠KPR into half. Given that LP and KQ are straight lines, ∠JKP = 41°, ∠PQN = 34° and ∠KNL = 115°, find
- ∠x
- ∠z
- ∠y
(a)
∠PNQ = ∠KNL = 115° (Vertically opposite angles)
∠x
= 180° - 115° - 34°
= 31° (Angles sum of triangle)
(b)
∠z
= 180° - 31°
= 149° (Interior angles)
(c)
∠y
= 180° - 31° - 31° - 34°
= 105° (Angles sum of triangle)
Answer(s): (a) 31°; (b) 149°; (c) 105°