The figure is not drawn to scale. XY//AZ and ZY//BX. Triangles XBY and YZA are isosceles triangles. Find
- ∠p
- ∠q.
(a)
∠YZA = ∠YXB = 74° (ZY//BX, YX//ZA)
∠XYB
= (180° - 74°) ÷ 2
= 106° ÷ 2
= 53° (Isosceles triangle)
∠ZYA
= 180° - 74° - 74°
= 32° (Isosceles triangle)
∠p
= 180° - 74° - 53° - 32°
= 21° (Interior angles, YX//ZA)
(b)
∠q
= 180° - 26° - 21°
= 133° (Angles sum of triangle)
Answer(s): (a) 21°; (b) 133°