In the figure, MNP is parallel to STU and the line SP cuts ∠NSU into half. Given that PS and NT are straight lines, ∠MNS = 46°, ∠STR = 32° and ∠NRP = 117°, find
- ∠q
- ∠s
- ∠r
(a)
∠SRT = ∠NRP = 117° (Vertically opposite angles)
∠q
= 180° - 117° - 32°
= 31° (Angles sum of triangle)
(b)
∠s
= 180° - 31°
= 149° (Interior angles)
(c)
∠r
= 180° - 31° - 31° - 32°
= 102° (Angles sum of triangle)
Answer(s): (a) 31°; (b) 149°; (c) 102°