In the figure, BCDE is a parallelogram. DG, GH and BC are straight lines. BEF is an isosceles triangle.
- Find ∠b.
- Find ∠c.
(a)
∠DGB = ∠CBH = 65° (Corresponding angles, BC//GD)
∠GFB
= 180° - ∠DGB - ∠GBF
= 180° - 65° - 15°
= 100° (Angles sum of triangle)
∠EFB
= 180° - 100°
= 80° (Angles on a straight line)
∠FEB = ∠EFB = 80° (Isosceles triangle)
∠b
= ∠FEB
= 80° (Corresponding angles, CD//BE)
(b)
∠c
= 180° - 80° - 80°
= 20° (Isosceles triangle BEF)
Answer(s): (a) 80°; (b) 20°