In the figure, QRST is a parallelogram. SV, VW and QR are straight lines. QTU is an isosceles triangle.
- Find ∠q.
- Find ∠r.
(a)
∠SVQ = ∠RQW = 61° (Corresponding angles, QR//VS)
∠VUQ
= 180° - ∠SVQ - ∠VQU
= 180° - 61° - 16°
= 103° (Angles sum of triangle)
∠TUQ
= 180° - 103°
= 77° (Angles on a straight line)
∠UTQ = ∠TUQ = 77° (Isosceles triangle)
∠q
= ∠UTQ
= 77° (Corresponding angles, RS//QT)
(b)
∠r
= 180° - 77° - 77°
= 26° (Isosceles triangle QTU)
Answer(s): (a) 77°; (b) 26°