Question

In the following figure, AB || CD, AF || ED, ∠AFC = 68° and ∠FED = 42°. Find ∠EFD.

Answer 1

We have,

Since, AF || ED and FD is a transversal.

∴ ∠3 = 68°  ...(i) [Corresponding angles]

Now, AB || CD and ED is a transversal.

∴ (∠2 + 42°) + ∠3 = 180°  ...[Co-interior angles]

⇒ ∠2 = 180° – 42° – 68°   ...[Using (i)]

⇒ ∠2 = 70°   ...(ii)

Also, AB || CD and EF is a transversal.

∴ ∠1 = ∠2  ...[Alternate interior angles]

⇒ ∠1 = 70°  ...[Using (ii)]

Thus, ∠EFD = 70°