PSLEQRST is a parallelogram, QSU is an equilateral triangle and ST = TU.
- Find ∠QST.
- Find ∠STQ.
- Find ∠UQR.
(a)
ST = TU
Triangle STU is an isosceles triangle.
∠TSU
= (180° - 146°) ÷ 2
= 34° ÷ 2
= 17° (Isosceles triangle)
∠QST
= 60° - 17°
= 43° (Equilateral triangle)
(b)
∠QUT
= 60° - 17°
= 43° (Equilateral triangle)
∠QTU
= 180° - 43° - 17°
= 120° (Angles sum of triangle)
∠QTS
= 360° - 146° - 120°
= 94° (Angles at a point)
∠RQS
= ∠QST
= 43° (Alternate angles)
∠RQU
= 60° + 43°
= 103°
Answer(s): (a) 43°; (b) 94°; (c) 103°