The figure is not drawn to scale. UVXY is a parallelogram. ∠YUO is 58° and ∠XVW is 32°. UVW is an isosceles triangle and UV = VW.
- Find ∠OWV.
- Find ∠UYX.
(a)
∠VOU = 58° (Alternate angles, UY//VX)
∠VOW
= 180° - 58°
= 122° (Angles on a straight line)
∠OWV
= 180° - 122° - 32°
= 26° (Angles sum of triangle)
(b)
∠VUO = 26° (Isosceles triangle UVW)
∠UYX
= 180° - 58° - 26°
= 96° (Interior angles, UV//YX)
Answer(s): (a) 26°; (b) 96°