In Fig 8.121, arms BA and BC of ∠ABC are respectively parallel to arms ED and EF of ∠DEF. Prove that ∠ABC + ∠DEF = 180°

Given that,

AB ‖ DE and 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 angles) (i)

Also,

EF ‖ ML and EM is the transversal

By the property co interior angles are supplementary

∠DEF + ∠EML = 180^o(ii)

From (i) and (ii), we have

∠DEF + ∠ABC = 180^o

Hence, proved