Question

In the given figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that ∠ROS = $\frac{1}{2}$ (∠QOS − POS).

Answer 1

The given figure is as follows:

We have POQ as a line. Ray OR is perpendicular to line PQ. Therefore,

From the figure above, we get:

(i)

and form a linear pair. Therefore,

(ii)

From (i) and (ii) equation we get:
$\angle QOS+\angle POS=2\times 90$

Hence proved.