In the figure, EFGH is a parallelogram. GK, KL and EF are straight lines. EHJ is an isosceles triangle.
- Find ∠k.
- Find ∠m.
(a)
∠GKE = ∠FEL = 66° (Corresponding angles, EF//KG)
∠KJE
= 180° - ∠GKE - ∠KEJ
= 180° - 66° - 16°
= 98° (Angles sum of triangle)
∠HJE
= 180° - 98°
= 82° (Angles on a straight line)
∠JHE = ∠HJE = 82° (Isosceles triangle)
∠k
= ∠JHE
= 82° (Corresponding angles, FG//EH)
(b)
∠m
= 180° - 82° - 82°
= 16° (Isosceles triangle EHJ)
Answer(s): (a) 82°; (b) 16°