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° - 144°) ÷ 2
= 36° ÷ 2
= 18° (Isosceles triangle)
∠QST
= 60° - 18°
= 42° (Equilateral triangle)
(b)
∠QUT
= 60° - 18°
= 42° (Equilateral triangle)
∠QTU
= 180° - 42° - 18°
= 120° (Angles sum of triangle)
∠QTS
= 360° - 144° - 120°
= 96° (Angles at a point)
∠RQS
= ∠QST
= 42° (Alternate angles)
∠RQU
= 60° + 42°
= 102°
Answer(s): (a) 42°; (b) 96°; (c) 102°