PSLEPQRS is a parallelogram, PRT is an equilateral triangle and RS = ST.
- Find ∠PRS.
- Find ∠RSP.
- Find ∠TPQ.
(a)
RS = ST
Triangle RST is an isosceles triangle.
∠SRT
= (180° - 130°) ÷ 2
= 50° ÷ 2
= 25° (Isosceles triangle)
∠PRS
= 60° - 25°
= 35° (Equilateral triangle)
(b)
∠PTS
= 60° - 25°
= 35° (Equilateral triangle)
∠PST
= 180° - 35° - 25°
= 120° (Angles sum of triangle)
∠PSR
= 360° - 130° - 120°
= 110° (Angles at a point)
∠QPR
= ∠PRS
= 35° (Alternate angles)
∠QPT
= 60° + 35°
= 95°
Answer(s): (a) 35°; (b) 110°; (c) 95°