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

Question:

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

 

Solution:

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°     

 

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