In the figure, QRST is a parallelogram. SV, VW and QR are straight lines. QTU is an isosceles triangle.
- Find ∠a.
- Find ∠b.
(a)
∠SVQ = ∠RQW = 60° (Corresponding angles, QR//VS)
∠VUQ
= 180° - ∠SVQ - ∠VQU
= 180° - 60° - 16°
= 104° (Angles sum of triangle)
∠TUQ
= 180° - 104°
= 76° (Angles on a straight line)
∠UTQ = ∠TUQ = 76° (Isosceles triangle)
∠a
= ∠UTQ
= 76° (Corresponding angles, RS//QT)
(b)
∠b
= 180° - 76° - 76°
= 28° (Isosceles triangle QTU)
Answer(s): (a) 76°; (b) 28°