In the figure, PQRS is a parallelogram. RU, UV and PQ are straight lines. PST is an isosceles triangle.
- Find ∠v.
- Find ∠w.
(a)
∠RUP = ∠QPV = 59° (Corresponding angles, PQ//UR)
∠UTP
= 180° - ∠RUP - ∠UPT
= 180° - 59° - 16°
= 105° (Angles sum of triangle)
∠STP
= 180° - 105°
= 75° (Angles on a straight line)
∠TSP = ∠STP = 75° (Isosceles triangle)
∠v
= ∠TSP
= 75° (Corresponding angles, QR//PS)
(b)
∠w
= 180° - 75° - 75°
= 30° (Isosceles triangle PST)
Answer(s): (a) 75°; (b) 30°