In the given figure, prove that AB || CD.

∠CEF = 30° + 50° = 80°

∠DCE = 80° (Given)

∠CEF = ∠DCE

But these are alternate interior angle.

CD || EF ……(i)

Now ∠EAB = 130° (Given)

∠AEF = 50° (Given)

∠EAB + ∠AEF = 130° + 50° = 180°

But these are co-interior angles.

AB || EF …(ii)

From eq. (i) and (ii), we get

AB || CD || EF

Hence, AB || CD

Co-interior angles/Allied angles: Sum of interior angles on the same side of transversal is 180°.