In the figure, QRST is a parallelogram. SV, VW and QR are straight lines. QTU is an isosceles triangle.
- Find ∠k.
- Find ∠m.
(a)
∠SVQ = ∠RQW = 64° (Corresponding angles, QR//VS)
∠VUQ
= 180° - ∠SVQ - ∠VQU
= 180° - 64° - 18°
= 98° (Angles sum of triangle)
∠TUQ
= 180° - 98°
= 82° (Angles on a straight line)
∠UTQ = ∠TUQ = 82° (Isosceles triangle)
∠k
= ∠UTQ
= 82° (Corresponding angles, RS//QT)
(b)
∠m
= 180° - 82° - 82°
= 16° (Isosceles triangle QTU)
Answer(s): (a) 82°; (b) 16°