Question

Question #ca751

Answer 1

`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!!!]