The figure is not drawn to scale. RSUV is a parallelogram. ∠VRO is 57° and ∠UST is 27°. RST is an isosceles triangle and RS = ST.
- Find ∠OTS.
- Find ∠RVU.
(a)
∠SOR = 57° (Alternate angles, RV//SU)
∠SOT
= 180° - 57°
= 123° (Angles on a straight line)
∠OTS
= 180° - 123° - 27°
= 30° (Angles sum of triangle)
(b)
∠SRO = 30° (Isosceles triangle RST)
∠RVU
= 180° - 57° - 30°
= 93° (Interior angles, RS//VU)
Answer(s): (a) 30°; (b) 93°