In the figure, ABCD is a parallelogram. CF, FG and AB are straight lines. ADE is an isosceles triangle.
- Find ∠x.
- Find ∠y.
(a)
∠CFA = ∠BAG = 59° (Corresponding angles, AB//FC)
∠FEA
= 180° - ∠CFA - ∠FAE
= 180° - 59° - 15°
= 106° (Angles sum of triangle)
∠DEA
= 180° - 106°
= 74° (Angles on a straight line)
∠EDA = ∠DEA = 74° (Isosceles triangle)
∠x
= ∠EDA
= 74° (Corresponding angles, BC//AD)
(b)
∠y
= 180° - 74° - 74°
= 32° (Isosceles triangle ADE)
Answer(s): (a) 74°; (b) 32°