Question

In the below fig, arms BA and BC of ∠ABC are respectively parallel to arms ED and EF of ∠DEF. Prove that ∠ABC + ∠DEF = 180°.

Answer 1

Given AB || DE, BC || EF 

To prove: ∠ABC +∠DEF = 180^o 

Construction: produce BC to intersect DE at M 

Proof: Since AB || EM and BL is the transversal 

∠ABC = ∠EML [Corresponding angle] ……(i) 

Also, EF || ML and EM is the transversal 

By the property of co-interior angles are supplementary 

∠DEF + ∠EML = 180^o ...........(ii)

From (i) and (ii) we have 

∠DEF + ∠ABC =180^o