In the figure, ABCD is a parallelogram. CF, FG and AB are straight lines. ADE is an isosceles triangle.
- Find ∠j.
- Find ∠k.
(a)
∠CFA = ∠BAG = 59° (Corresponding angles, AB//FC)
∠FEA
= 180° - ∠CFA - ∠FAE
= 180° - 59° - 16°
= 105° (Angles sum of triangle)
∠DEA
= 180° - 105°
= 75° (Angles on a straight line)
∠EDA = ∠DEA = 75° (Isosceles triangle)
∠j
= ∠EDA
= 75° (Corresponding angles, BC//AD)
(b)
∠k
= 180° - 75° - 75°
= 30° (Isosceles triangle ADE)
Answer(s): (a) 75°; (b) 30°