The figure is not drawn to scale. XY//AZ and ZY//BX. Triangles XBY and YZA are isosceles triangles. Find
- ∠m
- ∠n.
(a)
∠YZA = ∠YXB = 76° (ZY//BX, YX//ZA)
∠XYB
= (180° - 76°) ÷ 2
= 104° ÷ 2
= 52° (Isosceles triangle)
∠ZYA
= 180° - 76° - 76°
= 28° (Isosceles triangle)
∠m
= 180° - 76° - 52° - 28°
= 24° (Interior angles, YX//ZA)
(b)
∠n
= 180° - 26° - 24°
= 130° (Angles sum of triangle)
Answer(s): (a) 24°; (b) 130°