In the figure, PQRS is a parallelogram. RU, UV and PQ are straight lines. PST is an isosceles triangle.
- Find ∠y.
- Find ∠z.
(a)
∠RUP = ∠QPV = 59° (Corresponding angles, PQ//UR)
∠UTP
= 180° - ∠RUP - ∠UPT
= 180° - 59° - 21°
= 100° (Angles sum of triangle)
∠STP
= 180° - 100°
= 80° (Angles on a straight line)
∠TSP = ∠STP = 80° (Isosceles triangle)
∠y
= ∠TSP
= 80° (Corresponding angles, QR//PS)
(b)
∠z
= 180° - 80° - 80°
= 20° (Isosceles triangle PST)
Answer(s): (a) 80°; (b) 20°