PSLE In the figure, RSTU is a parallelogram. PUR and QUT are straight lines and PQ = QR. ∠PQU = 30° and ∠STU = 57°.
- Find ∠TUR.
- Find ∠UQR.
(a)
∠TUR
= 180° - 57°
= 123° (Interior angles)
(b)
∠PUQ
= ∠TUR
= 123° (Vertically opposite angles)
∠QPU
= 180° - 123° - 30°
= 27° (Angles sum of triangle)
∠QRU = ∠QPU (Isosceles triangle)
∠PQR
= 180° - 27° - 27°
= 126° (Angles sum of triangle)
∠UQR
= 126° - 30°
= 96°
Answer(s): (a) 123°; (b) 96°