Question

In the given figure AB||DE prove that

Answer 1

∠ ABC + ∠ BCD = 180° + ∠ CDE (Proved)

Step-by-step explanation:

See the attached diagram.

Draw a line parallel to AB and DE through C which is GH and extend AB to F.

Now, ∠ ABC = 180° - ∠ CBF = 180° - ∠BCG

{Since, ∠ CBF and ∠ BCG are alternate angles as AF ║ GH and BC is transverse }

And ∠ BCD = ∠ BCG + ∠ GCD

So, ∠ ABC + ∠ BCD = (180° - ∠ BCG) + (∠ BCG + ∠ GCD) = 180° + ∠ GCD

Now, ∠ GCD = ∠ CDE

{Alternate angles, as DE ║ GH and DC is transverse}

So, ∠ ABC + ∠ BCD = 180° + ∠ CDE (Proved)