Question

In the given figure, AB || CD and P is any point shown in the figure. Prove that:
∠ABP + ∠BPD + ∠CDP = 360°

Answer 1

The given figure is as follows:

It is give that

Let us draw a line passing through point P and parallel to AB and CD.

We have, thus, and are consecutive interior angles. Therefore,

(i)

Similarly, we have , thus, and are consecutive interior angles. Therefore,

(ii)

On adding equation (i) and (ii), we get:

Hence proved .