The figure is not drawn to scale. QSTU is a trapezium and QS // UT. Given that QU = QR, ∠UQR = 72° and ∠QST = 103°.
- Find ∠STU
- Find ∠QRU
- Find ∠RUT
(a)
∠STU
= 180° - 103°
= 77° (Interior angles, QS//UT)
(b)
∠QRU
= (180° - 72°) ÷ 2
= 108° ÷ 2
= 54° (Isosceles triangle)
(c)
∠RUT
= ∠QRU
= 54° (Alternate angles, QS//UT)
Answer(s): (a) 77°; (b) 54°; (c) 54°