In the figure, PQRS is a parallelogram. RU, UV and PQ are straight lines. PST is an isosceles triangle.
- Find ∠k.
- Find ∠m.
(a)
∠RUP = ∠QPV = 64° (Corresponding angles, PQ//UR)
∠UTP
= 180° - ∠RUP - ∠UPT
= 180° - 64° - 21°
= 95° (Angles sum of triangle)
∠STP
= 180° - 95°
= 85° (Angles on a straight line)
∠TSP = ∠STP = 85° (Isosceles triangle)
∠k
= ∠TSP
= 85° (Corresponding angles, QR//PS)
(b)
∠m
= 180° - 85° - 85°
= 10° (Isosceles triangle PST)
Answer(s): (a) 85°; (b) 10°