In the figure, MNPQ is a parallelogram. PS, ST and MN are straight lines. MQR is an isosceles triangle.
- Find ∠w.
- Find ∠x.
(a)
∠PSM = ∠NMT = 64° (Corresponding angles, MN//SP)
∠SRM
= 180° - ∠PSM - ∠SMR
= 180° - 64° - 15°
= 101° (Angles sum of triangle)
∠QRM
= 180° - 101°
= 79° (Angles on a straight line)
∠RQM = ∠QRM = 79° (Isosceles triangle)
∠w
= ∠RQM
= 79° (Corresponding angles, NP//MQ)
(b)
∠x
= 180° - 79° - 79°
= 22° (Isosceles triangle MQR)
Answer(s): (a) 79°; (b) 22°