Question

In the given figure, BA || ED and BC || EF. Show that $\angle ABC+\angle DEF={180}^{\circ }$.

Answer 1

ANSWER:
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°