The figure is not drawn to scale. XY//AZ and ZY//BX. Triangles XBY and YZA are isosceles triangles. Find
- ∠v
- ∠w.
(a)
∠YZA = ∠YXB = 74° (ZY//BX, YX//ZA)
∠XYB
= (180° - 74°) ÷ 2
= 106° ÷ 2
= 53° (Isosceles triangle)
∠ZYA
= 180° - 74° - 74°
= 32° (Isosceles triangle)
∠v
= 180° - 74° - 53° - 32°
= 21° (Interior angles, YX//ZA)
(b)
∠w
= 180° - 28° - 21°
= 131° (Angles sum of triangle)
Answer(s): (a) 21°; (b) 131°