Question

In the given figure, BA || ED and BC || EF. Show that ∠ABC + ∠DEF = 180°.

Answer 1

It is given that, BA || ED and BC || EF.

Construction: Extend ED such that it intersects BC at G.



Now, BA || GE and BC is a transversal.

∴ ∠ABC = ∠EGC .....(1) (Pair of corresponding angles)

Also, BC || EF and EG is a transversal.

∴ ∠EGC + ∠GEF = 180° .....(2) (Interior angles on the same side of the transversal are supplementary)

From (1) and (2), we have

​∠ABC + ∠GEF = 180°

Or ∠ABC + ∠DEF = 180°