The figure is not drawn to scale. TUWX is a parallelogram. ∠XTO is 58° and ∠WUV is 26°. TUV is an isosceles triangle and TU = UV.
- Find ∠OVU.
- Find ∠TXW.
(a)
∠UOT = 58° (Alternate angles, TX//UW)
∠UOV
= 180° - 58°
= 122° (Angles on a straight line)
∠OVU
= 180° - 122° - 26°
= 32° (Angles sum of triangle)
(b)
∠UTO = 32° (Isosceles triangle TUV)
∠TXW
= 180° - 58° - 32°
= 90° (Interior angles, TU//XW)
Answer(s): (a) 32°; (b) 90°