In triangle OPQ,
OP = OQ [Given]
therefore angle OPQ = angle OQP = 30^@ [Given, angle OPQ = 30^@]
That means, angle POQ = 180^@ - (30 + 30)^@ = 120^@
From the figure, it is clear that angle POQ and angle POS are supplementary.
therefore angle POS = 180^@ - 120^@ = 60^@
In triangle OPS,
OP = OS [Given]
therefore angle OPS = angle OSP
We know, angle POS + angle OPS + angle OSP = 180^@
rArr angle OPS + angle OSP = 180^@ - 60^@ [angle POS = 60^@]
rArr 2angle OSP = 120^@ [angle OPS = angle OSP]
rArr angle OSP = 60^@
Hence Explained.
This proves that The quadrilateral is also a rectangle. [Interesting Property!!!]