In the figure, MNPQ is a parallelogram. PS, ST and MN are straight lines. MQR is an isosceles triangle.
- Find ∠x.
- Find ∠y.
(a)
∠PSM = ∠NMT = 65° (Corresponding angles, MN//SP)
∠SRM
= 180° - ∠PSM - ∠SMR
= 180° - 65° - 15°
= 100° (Angles sum of triangle)
∠QRM
= 180° - 100°
= 80° (Angles on a straight line)
∠RQM = ∠QRM = 80° (Isosceles triangle)
∠x
= ∠RQM
= 80° (Corresponding angles, NP//MQ)
(b)
∠y
= 180° - 80° - 80°
= 20° (Isosceles triangle MQR)
Answer(s): (a) 80°; (b) 20°