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° - 134°) ÷ 2
= 46° ÷ 2
= 23° (Isosceles triangle)
∠PRS
= 60° - 23°
= 37° (Equilateral triangle)
(b)
∠PTS
= 60° - 23°
= 37° (Equilateral triangle)
∠PST
= 180° - 37° - 23°
= 120° (Angles sum of triangle)
∠PSR
= 360° - 134° - 120°
= 106° (Angles at a point)
∠QPR
= ∠PRS
= 37° (Alternate angles)
∠QPT
= 60° + 37°
= 97°
Answer(s): (a) 37°; (b) 106°; (c) 97°
