In the figure, BCDE is a parallelogram. DG, GH and BC are straight lines. BEF is an isosceles triangle.
- Find ∠k.
- Find ∠m.
(a)
∠DGB = ∠CBH = 61° (Corresponding angles, BC//GD)
∠GFB
= 180° - ∠DGB - ∠GBF
= 180° - 61° - 16°
= 103° (Angles sum of triangle)
∠EFB
= 180° - 103°
= 77° (Angles on a straight line)
∠FEB = ∠EFB = 77° (Isosceles triangle)
∠k
= ∠FEB
= 77° (Corresponding angles, CD//BE)
(b)
∠m
= 180° - 77° - 77°
= 26° (Isosceles triangle BEF)
Answer(s): (a) 77°; (b) 26°