In the figure, STUV is a parallelogram. UX, XY and ST are straight lines. SVW is an isosceles triangle.
- Find ∠r.
- Find ∠s.
(a)
∠UXS = ∠TSY = 66° (Corresponding angles, ST//XU)
∠XWS
= 180° - ∠UXS - ∠XSW
= 180° - 66° - 17°
= 97° (Angles sum of triangle)
∠VWS
= 180° - 97°
= 83° (Angles on a straight line)
∠WVS = ∠VWS = 83° (Isosceles triangle)
∠r
= ∠WVS
= 83° (Corresponding angles, TU//SV)
(b)
∠s
= 180° - 83° - 83°
= 14° (Isosceles triangle SVW)
Answer(s): (a) 83°; (b) 14°