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 = 65° (Corresponding angles, PQ//UR)
∠UTP
= 180° - ∠RUP - ∠UPT
= 180° - 65° - 18°
= 97° (Angles sum of triangle)
∠STP
= 180° - 97°
= 83° (Angles on a straight line)
∠TSP = ∠STP = 83° (Isosceles triangle)
∠k
= ∠TSP
= 83° (Corresponding angles, QR//PS)
(b)
∠m
= 180° - 83° - 83°
= 14° (Isosceles triangle PST)
Answer(s): (a) 83°; (b) 14°