In the figure, PQRS is a parallelogram. RU, UV and PQ are straight lines. PST is an isosceles triangle.
- Find ∠c.
- Find ∠d.
(a)
∠RUP = ∠QPV = 58° (Corresponding angles, PQ//UR)
∠UTP
= 180° - ∠RUP - ∠UPT
= 180° - 58° - 21°
= 101° (Angles sum of triangle)
∠STP
= 180° - 101°
= 79° (Angles on a straight line)
∠TSP = ∠STP = 79° (Isosceles triangle)
∠c
= ∠TSP
= 79° (Corresponding angles, QR//PS)
(b)
∠d
= 180° - 79° - 79°
= 22° (Isosceles triangle PST)
Answer(s): (a) 79°; (b) 22°