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° - 134°) ÷ 2
= 46° ÷ 2
= 23° (Isosceles triangle)
∠QST
= 60° - 23°
= 37° (Equilateral triangle)
(b)
∠QUT
= 60° - 23°
= 37° (Equilateral triangle)
∠QTU
= 180° - 37° - 23°
= 120° (Angles sum of triangle)
∠QTS
= 360° - 134° - 120°
= 106° (Angles at a point)
∠RQS
= ∠QST
= 37° (Alternate angles)
∠RQU
= 60° + 37°
= 97°
Answer(s): (a) 37°; (b) 106°; (c) 97°