The figure is not drawn to scale. TUWX is a parallelogram. ∠XTO is 59° and ∠WUV is 28°. TUV is an isosceles triangle and TU = UV.
- Find ∠OVU.
- Find ∠TXW.
(a)
∠UOT = 59° (Alternate angles, TX//UW)
∠UOV
= 180° - 59°
= 121° (Angles on a straight line)
∠OVU
= 180° - 121° - 28°
= 31° (Angles sum of triangle)
(b)
∠UTO = 31° (Isosceles triangle TUV)
∠TXW
= 180° - 59° - 31°
= 90° (Interior angles, TU//XW)
Answer(s): (a) 31°; (b) 90°