In the figure, NPQ is parallel to RST and RQ cuts ∠PRS equally. Given that ∠NPR = 48° and ∠PUQ = 110°, find
- ∠q
- ∠r
(a)
∠NPR = ∠PRS (Alternate angles)
∠q
= 48° ÷ 2
= 24°
(b)
∠PRU = ∠q = 24°
∠r
= 110° - 24°
= 86° (Exterior angle of a triangle)
Answer(s): (a) 24°; (b) 86°