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!!!]
