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 = 60° (Corresponding angles, MN//SP)
∠SRM
= 180° - ∠PSM - ∠SMR
= 180° - 60° - 18°
= 102° (Angles sum of triangle)
∠QRM
= 180° - 102°
= 78° (Angles on a straight line)
∠RQM = ∠QRM = 78° (Isosceles triangle)
∠w
= ∠RQM
= 78° (Corresponding angles, NP//MQ)
(b)
∠x
= 180° - 78° - 78°
= 24° (Isosceles triangle MQR)
Answer(s): (a) 78°; (b) 24°
