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In the given figure, O is the centre of ...

In the given figure, O is the centre of the circle and PQ is one of its diamtere, then the value of x is

A

140

B

40

C

80

D

20

Text Solution

Verified by Experts

The correct Answer is:
D
In the given figure, `angle POR=140^(@)` ( Given)
`:. angle ROQ=180^(@)-140^(@)=40^(@)`
Now, the angle in circle produced by the are `overset (frown)(QR)`
`angle QSR `and the central angle `=angleROQ`
`:. angleQSR=(1)/(2) angleROQ`[ by theorem -34) `=(1)/(2)xx40^(@)=20^(@)`
`:.x^(@)=angleQSR=20^(@), :.x=20`
`:. (d)` is correct
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