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° - 130°) ÷ 2
= 50° ÷ 2
= 25° (Isosceles triangle)
∠QST
= 60° - 25°
= 35° (Equilateral triangle)
(b)
∠QUT
= 60° - 25°
= 35° (Equilateral triangle)
∠QTU
= 180° - 35° - 25°
= 120° (Angles sum of triangle)
∠QTS
= 360° - 130° - 120°
= 110° (Angles at a point)
∠RQS
= ∠QST
= 35° (Alternate angles)
∠RQU
= 60° + 35°
= 95°
Answer(s): (a) 35°; (b) 110°; (c) 95°
