In the figure, $OP, OQ, OR$ and $OS$ are four rays. Prove that: $\angle POQ + \angle QOR + \angle SOR + \angle POS = 360^o$.
"
Given:
$OP, OQ, OR$ and $OS$ are four rays.
To do:
We have to prove that $\angle POQ + \angle QOR + \angle SOR + \angle POS = 360^o$.
Solution:
Produce $PO$ to $E$
Therefore,
$\angle POQ + \angle QOE = 180^o$.......(i) (Linear pair)
Similarly,
$\angle EOS + \angle POS = 180^o$......(ii)
Adding (i) and (ii), we get,
$\angle POQ + \angle QOR + \angle ROE + \angle EOS + \angle POS = 180^o + 180^o$
$\angle POQ + \angle QOR + \angle ROS + \angle POS = 360^o$
$\angle POQ + \angle QOR + \angle SOR + \angle POS = 360^o$
Hence proved.
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