Question

In the given figure AB parallel DE Prove that angle ABC + angle BCD= 180° + angle CDE

Answer 1

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draw a line parallel to AB as PQ

EDC = DCP (alternative interior angle)
PCB + ABC = 180 (supplements)

ABC + BCP = 180
ABC + BCP + PCD = 180 + CDE (PCD = CDE)
ABC + BCD = 180 + CDE


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Answer 2

Answer:

Step-by-step explanation:

Given information: BA║ED

To prove:  

Proof:

Draw a line PC, such that PC║BA and PC║ED.

If transversal line intersect two parallel lines, then alternate interior angle are same.

Since PC║ED, and DC is a transversal line, so

               .... (1)

From the given figure it is clear that line PC divides the angle BCD in two parts.

       .... (2)

If transversal line intersect two parallel lines, then the sum of  same sided interior angles is 180°.

Since PC║AB, and BC is a transversal line, so

Using equation (2) we get

             

Add  on both sides.

Using equation (1) we get

           

Hence proved.