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 = 47°, ∠STR = 35° and ∠NRP = 116°, find
- ∠x
- ∠z
- ∠y
(a)
∠SRT = ∠NRP = 116° (Vertically opposite angles)
∠x
= 180° - 116° - 35°
= 29° (Angles sum of triangle)
(b)
∠z
= 180° - 29°
= 151° (Interior angles)
(c)
∠y
= 180° - 29° - 29° - 35°
= 98° (Angles sum of triangle)
Answer(s): (a) 29°; (b) 151°; (c) 98°