In the figure, STUV is a parallelogram. UX, XY and ST are straight lines. SVW is an isosceles triangle.
- Find ∠d.
- Find ∠e.
(a)
∠UXS = ∠TSY = 58° (Corresponding angles, ST//XU)
∠XWS
= 180° - ∠UXS - ∠XSW
= 180° - 58° - 16°
= 106° (Angles sum of triangle)
∠VWS
= 180° - 106°
= 74° (Angles on a straight line)
∠WVS = ∠VWS = 74° (Isosceles triangle)
∠d
= ∠WVS
= 74° (Corresponding angles, TU//SV)
(b)
∠e
= 180° - 74° - 74°
= 32° (Isosceles triangle SVW)
Answer(s): (a) 74°; (b) 32°