In the figure, BCDE is a parallelogram. DG, GH and BC are straight lines. BEF is an isosceles triangle.
- Find ∠q.
- Find ∠r.
(a)
∠DGB = ∠CBH = 60° (Corresponding angles, BC//GD)
∠GFB
= 180° - ∠DGB - ∠GBF
= 180° - 60° - 21°
= 99° (Angles sum of triangle)
∠EFB
= 180° - 99°
= 81° (Angles on a straight line)
∠FEB = ∠EFB = 81° (Isosceles triangle)
∠q
= ∠FEB
= 81° (Corresponding angles, CD//BE)
(b)
∠r
= 180° - 81° - 81°
= 18° (Isosceles triangle BEF)
Answer(s): (a) 81°; (b) 18°
