The figure is not drawn to scale. XY//AZ and ZY//BX. Triangles XBY and YZA are isosceles triangles. Find
- ∠y
- ∠z.
(a)
∠YZA = ∠YXB = 70° (ZY//BX, YX//ZA)
∠XYB
= (180° - 70°) ÷ 2
= 110° ÷ 2
= 55° (Isosceles triangle)
∠ZYA
= 180° - 70° - 70°
= 40° (Isosceles triangle)
∠y
= 180° - 70° - 55° - 40°
= 15° (Interior angles, YX//ZA)
(b)
∠z
= 180° - 27° - 15°
= 138° (Angles sum of triangle)
Answer(s): (a) 15°; (b) 138°