Question

In the given figure, OP, OQ, OR and OS are four rays. Prove that:
∠POQ + ∠QOR + ∠SOR + ∠POS = 360°

Answer 1

Let us draw as a straight line.

Since,is a line, therefore,, and form a linear pair.

Also, and form a linear pair.

Thus, we have:

(i)

And

(ii)

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

Hence proved.