In the figure, QRST is a parallelogram. SV, VW and QR are straight lines. QTU is an isosceles triangle.
- Find ∠w.
- Find ∠x.
(a)
∠SVQ = ∠RQW = 60° (Corresponding angles, QR//VS)
∠VUQ
= 180° - ∠SVQ - ∠VQU
= 180° - 60° - 20°
= 100° (Angles sum of triangle)
∠TUQ
= 180° - 100°
= 80° (Angles on a straight line)
∠UTQ = ∠TUQ = 80° (Isosceles triangle)
∠w
= ∠UTQ
= 80° (Corresponding angles, RS//QT)
(b)
∠x
= 180° - 80° - 80°
= 20° (Isosceles triangle QTU)
Answer(s): (a) 80°; (b) 20°