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 = 48°, ∠QRP = 39° and ∠LPM = 117°, find
- ∠k
- ∠n
- ∠m
(a)
∠QPR = ∠LPM = 117° (Vertically opposite angles)
∠k
= 180° - 117° - 39°
= 24° (Angles sum of triangle)
(b)
∠n
= 180° - 24°
= 156° (Interior angles)
(c)
∠m
= 180° - 24° - 24° - 39°
= 93° (Angles sum of triangle)
Answer(s): (a) 24°; (b) 156°; (c) 93°