In the figure, BCDE is a parallelogram. DG, GH and BC are straight lines. BEF is an isosceles triangle.
- Find ∠a.
- Find ∠b.
(a)
∠DGB = ∠CBH = 64° (Corresponding angles, BC//GD)
∠GFB
= 180° - ∠DGB - ∠GBF
= 180° - 64° - 20°
= 96° (Angles sum of triangle)
∠EFB
= 180° - 96°
= 84° (Angles on a straight line)
∠FEB = ∠EFB = 84° (Isosceles triangle)
∠a
= ∠FEB
= 84° (Corresponding angles, CD//BE)
(b)
∠b
= 180° - 84° - 84°
= 12° (Isosceles triangle BEF)
Answer(s): (a) 84°; (b) 12°