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° - 146°) ÷ 2
= 34° ÷ 2
= 17° (Isosceles triangle)
∠PRS
= 60° - 17°
= 43° (Equilateral triangle)
(b)
∠PTS
= 60° - 17°
= 43° (Equilateral triangle)
∠PST
= 180° - 43° - 17°
= 120° (Angles sum of triangle)
∠PSR
= 360° - 146° - 120°
= 94° (Angles at a point)
∠QPR
= ∠PRS
= 43° (Alternate angles)
∠QPT
= 60° + 43°
= 103°
Answer(s): (a) 43°; (b) 94°; (c) 103°