The figure is not drawn to scale. QSTU is a trapezium and QS // UT. Given that QU = QR, ∠UQR = 74° and ∠QST = 98°.
- Find ∠STU
- Find ∠QRU
- Find ∠RUT
(a)
∠STU
= 180° - 98°
= 82° (Interior angles, QS//UT)
(b)
∠QRU
= (180° - 74°) ÷ 2
= 106° ÷ 2
= 53° (Isosceles triangle)
(c)
∠RUT
= ∠QRU
= 53° (Alternate angles, QS//UT)
Answer(s): (a) 82°; (b) 53°; (c) 53°