The figure is not drawn to scale. QRTU is a parallelogram. ∠UQO is 56° and ∠TRS is 30°. QRS is an isosceles triangle and QR = RS.
- Find ∠OSR.
- Find ∠QUT.
(a)
∠ROQ = 56° (Alternate angles, QU//RT)
∠ROS
= 180° - 56°
= 124° (Angles on a straight line)
∠OSR
= 180° - 124° - 30°
= 26° (Angles sum of triangle)
(b)
∠RQO = 26° (Isosceles triangle QRS)
∠QUT
= 180° - 56° - 26°
= 98° (Interior angles, QR//UT)
Answer(s): (a) 26°; (b) 98°