The figure is not drawn to scale. UVXY is a parallelogram. ∠YUO is 57° and ∠XVW is 25°. UVW is an isosceles triangle and UV = VW.
- Find ∠OWV.
- Find ∠UYX.
(a)
∠VOU = 57° (Alternate angles, UY//VX)
∠VOW
= 180° - 57°
= 123° (Angles on a straight line)
∠OWV
= 180° - 123° - 25°
= 32° (Angles sum of triangle)
(b)
∠VUO = 32° (Isosceles triangle UVW)
∠UYX
= 180° - 57° - 32°
= 91° (Interior angles, UV//YX)
Answer(s): (a) 32°; (b) 91°