In the figure, PQRS is a parallelogram. RU, UV and PQ are straight lines. PST is an isosceles triangle.
- Find ∠q.
- Find ∠r.
(a)
∠RUP = ∠QPV = 62° (Corresponding angles, PQ//UR)
∠UTP
= 180° - ∠RUP - ∠UPT
= 180° - 62° - 16°
= 102° (Angles sum of triangle)
∠STP
= 180° - 102°
= 78° (Angles on a straight line)
∠TSP = ∠STP = 78° (Isosceles triangle)
∠q
= ∠TSP
= 78° (Corresponding angles, QR//PS)
(b)
∠r
= 180° - 78° - 78°
= 24° (Isosceles triangle PST)
Answer(s): (a) 78°; (b) 24°