Question

In the given figure, lines AB and CD are parallel and P is any point as shown in the figure. Show that ∠ABP + ∠ CDP = ∠DPB.

Answer 1

The given figure is:

It is give that

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

We have , thus, and are alternate interior opposite angles. Therefore,

(i)

Similarly, we have, thus, and are alternate interior opposite angles. Therefore,

(ii)

On adding (i) and (ii):

Hence proved.