In the figure, VWXY is a parallelogram. XA, AB and VW are straight lines. VYZ is an isosceles triangle.
- Find ∠k.
- Find ∠m.
(a)
∠XAV = ∠WVB = 64° (Corresponding angles, VW//AX)
∠AZV
= 180° - ∠XAV - ∠AVZ
= 180° - 64° - 19°
= 97° (Angles sum of triangle)
∠YZV
= 180° - 97°
= 83° (Angles on a straight line)
∠ZYV = ∠YZV = 83° (Isosceles triangle)
∠k
= ∠ZYV
= 83° (Corresponding angles, WX//VY)
(b)
∠m
= 180° - 83° - 83°
= 14° (Isosceles triangle VYZ)
Answer(s): (a) 83°; (b) 14°