In the figure, DEFG is a parallelogram. FJ, JK and DE are straight lines. DGH is an isosceles triangle.
- Find ∠k.
- Find ∠m.
(a)
∠FJD = ∠EDK = 58° (Corresponding angles, DE//JF)
∠JHD
= 180° - ∠FJD - ∠JDH
= 180° - 58° - 18°
= 104° (Angles sum of triangle)
∠GHD
= 180° - 104°
= 76° (Angles on a straight line)
∠HGD = ∠GHD = 76° (Isosceles triangle)
∠k
= ∠HGD
= 76° (Corresponding angles, EF//DG)
(b)
∠m
= 180° - 76° - 76°
= 28° (Isosceles triangle DGH)
Answer(s): (a) 76°; (b) 28°