Q. 645.0( 1 Vote )

In figure, arms BA a

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°

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses