Question

In the above right sided figure BA ||DE . PROVE THAT angle abc plue angle bcd is equal to 180 degree plus angle cde

Answer 1

Answer:

Step-by-step explanation:

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

∠PCD = ∠CDE               .... (1)

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

∠BCP + ∠PCD =  ∠BCD

∠BCP = ∠BCD - ∠PCD     .... (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

∠ABC + ∠BCP = 180

Using equation (2) we get

∠ABC + (∠BCD  - ∠PCD) = 180        [∠BCP = BCD - ∠PCD]

             

Add ∠PCD on both sides.

Using equation (1) we get

∠ABC + ∠BCD = 180 + ∠CDE           [∠PCD = ∠CDE]

           

Hence proved

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