The figure is not drawn to scale. CD//FE and ED//GC. Triangles CGD and DEF are isosceles triangles. Find
- ∠a
- ∠b.
(a)
∠DEF = ∠DCG = 74° (ED//GC, DC//EF)
∠CDG
= (180° - 74°) ÷ 2
= 106° ÷ 2
= 53° (Isosceles triangle)
∠EDF
= 180° - 74° - 74°
= 32° (Isosceles triangle)
∠a
= 180° - 74° - 53° - 32°
= 21° (Interior angles, DC//EF)
(b)
∠b
= 180° - 28° - 21°
= 131° (Angles sum of triangle)
Answer(s): (a) 21°; (b) 131°