In the figure, MNPQ is a parallelogram. PS, ST and MN are straight lines. MQR is an isosceles triangle.
- Find ∠s.
- Find ∠t.
(a)
∠PSM = ∠NMT = 58° (Corresponding angles, MN//SP)
∠SRM
= 180° - ∠PSM - ∠SMR
= 180° - 58° - 15°
= 107° (Angles sum of triangle)
∠QRM
= 180° - 107°
= 73° (Angles on a straight line)
∠RQM = ∠QRM = 73° (Isosceles triangle)
∠s
= ∠RQM
= 73° (Corresponding angles, NP//MQ)
(b)
∠t
= 180° - 73° - 73°
= 34° (Isosceles triangle MQR)
Answer(s): (a) 73°; (b) 34°