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° - 140°) ÷ 2
= 40° ÷ 2
= 20° (Isosceles triangle)
∠PRS
= 60° - 20°
= 40° (Equilateral triangle)
(b)
∠PTS
= 60° - 20°
= 40° (Equilateral triangle)
∠PST
= 180° - 40° - 20°
= 120° (Angles sum of triangle)
∠PSR
= 360° - 140° - 120°
= 100° (Angles at a point)
∠QPR
= ∠PRS
= 40° (Alternate angles)
∠QPT
= 60° + 40°
= 100°
Answer(s): (a) 40°; (b) 100°; (c) 100°