Question

In Fig, CD intersects the line AB at F, ∠CFB = 50° and ∠EFA = ∠AFD. Find the measure of ∠EFC.

Answer 1

Let ∠EFA = x. 

Then ∠AFD = x. 

It is given that CD intersects line AB at F. 

Therefore, ∠CFB = ∠AFD (Vertically opposite angles) 

So, x = 50° 

But ∠EFA = ∠AFD which gives ∠EFA = 50°

Now ∠CFB + ∠EFA + ∠EFC = 180° [As AB is a straight line]. 

or, 50° + 50° + ∠EFC = 180° 

or, ∠EFC = 180° – 100° 

Thus, ∠EFC = 80°.