In the figure, KLM is parallel to QRS and the line QM cuts ∠LQS into half. Given that MQ and LR are straight lines, ∠KLQ = 46°, ∠QRP = 34° and ∠LPM = 114°, find
- ∠x
- ∠z
- ∠y
(a)
∠QPR = ∠LPM = 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°
= 100° (Angles sum of triangle)
Answer(s): (a) 32°; (b) 148°; (c) 100°