In the figure, STUV is a parallelogram. UX, XY and ST are straight lines. SVW is an isosceles triangle.
- Find ∠p.
- Find ∠q.
(a)
∠UXS = ∠TSY = 65° (Corresponding angles, ST//XU)
∠XWS
= 180° - ∠UXS - ∠XSW
= 180° - 65° - 19°
= 96° (Angles sum of triangle)
∠VWS
= 180° - 96°
= 84° (Angles on a straight line)
∠WVS = ∠VWS = 84° (Isosceles triangle)
∠p
= ∠WVS
= 84° (Corresponding angles, TU//SV)
(b)
∠q
= 180° - 84° - 84°
= 12° (Isosceles triangle SVW)
Answer(s): (a) 84°; (b) 12°