Question #ca751

1 Answer
Dec 24, 2017

60^@

Explanation:

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!!!]