The figure is not drawn to scale. QRTU is a parallelogram. ∠UQO is 54° and ∠TRS is 27°. QRS is an isosceles triangle and QR = RS.
- Find ∠OSR.
- Find ∠QUT.
(a)
∠ROQ = 54° (Alternate angles, QU//RT)
∠ROS
= 180° - 54°
= 126° (Angles on a straight line)
∠OSR
= 180° - 126° - 27°
= 27° (Angles sum of triangle)
(b)
∠RQO = 27° (Isosceles triangle QRS)
∠QUT
= 180° - 54° - 27°
= 99° (Interior angles, QR//UT)
Answer(s): (a) 27°; (b) 99°