The figure is not drawn to scale. XY//AZ and ZY//BX. Triangles XBY and YZA are isosceles triangles. Find
- ∠r
- ∠s.
(a)
∠YZA = ∠YXB = 78° (ZY//BX, YX//ZA)
∠XYB
= (180° - 78°) ÷ 2
= 102° ÷ 2
= 51° (Isosceles triangle)
∠ZYA
= 180° - 78° - 78°
= 24° (Isosceles triangle)
∠r
= 180° - 78° - 51° - 24°
= 27° (Interior angles, YX//ZA)
(b)
∠s
= 180° - 25° - 27°
= 128° (Angles sum of triangle)
Answer(s): (a) 27°; (b) 128°