In the figure, MNPQ is a parallelogram. PS, ST and MN are straight lines. MQR is an isosceles triangle.
- Find ∠k.
- Find ∠m.
(a)
∠PSM = ∠NMT = 66° (Corresponding angles, MN//SP)
∠SRM
= 180° - ∠PSM - ∠SMR
= 180° - 66° - 16°
= 98° (Angles sum of triangle)
∠QRM
= 180° - 98°
= 82° (Angles on a straight line)
∠RQM = ∠QRM = 82° (Isosceles triangle)
∠k
= ∠RQM
= 82° (Corresponding angles, NP//MQ)
(b)
∠m
= 180° - 82° - 82°
= 16° (Isosceles triangle MQR)
Answer(s): (a) 82°; (b) 16°