Q. 645.0( 1 Vote )

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

Answer :

Given: BA || ED and BC|| EF.

To Prove: ∠ABC + ∠DEF = 180° .

Construction: Produce FE to meet AB at E'.

Proof: BA || ED and FEE' is the transversal.

∠BE'E = ∠DEF……………..(i)

BC || E'EF and AB is the transversal.

∠ BE'E = E'BC………………(ii)

BC || E'EF and AB is the transversal.

∠E'BC + ∠BE'E = 180° [ Angles on the same side of the transversal are supplementary]

⇒ ∠ABC + ∠BE'E = 180° [∠E'BC = ∠ABC]

⇒ ∠ABC + ∠DEF = 180° [From (i) ∠BE'E = ∠DEF]

\\\\ ∠ABC + ∠DEF = 180°

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