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 = 50°, ∠QRP = 32° and ∠LPM = 117°, find
- ∠p
- ∠r
- ∠q
(a)
∠QPR = ∠LPM = 117° (Vertically opposite angles)
∠p
= 180° - 117° - 32°
= 31° (Angles sum of triangle)
(b)
∠r
= 180° - 31°
= 149° (Interior angles)
(c)
∠q
= 180° - 31° - 31° - 32°
= 98° (Angles sum of triangle)
Answer(s): (a) 31°; (b) 149°; (c) 98°