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 = 44°, ∠QRP = 36° and ∠LPM = 112°, find
- ∠a
- ∠c
- ∠b
(a)
∠QPR = ∠LPM = 112° (Vertically opposite angles)
∠a
= 180° - 112° - 36°
= 32° (Angles sum of triangle)
(b)
∠c
= 180° - 32°
= 148° (Interior angles)
(c)
∠b
= 180° - 32° - 32° - 36°
= 100° (Angles sum of triangle)
Answer(s): (a) 32°; (b) 148°; (c) 100°