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In the adjoining figur , O is the center...

In the adjoining figur , O is the center of the circle and AB is one of its diameter. ABCD is a cyclic quadrilateral in wich AB||DC and if `angleBAC=25^(@)` , then the value of `angleDAC` IS

A

`50^(@)`

B

`25^(@)`

C

`130^(@)`

D

`40^(@)`

Text Solution

Verified by Experts

AOB is a diameter of the circle , `thereforeangleACB` is a semicircular angle , `thereforeangleACB=90^(@)`
Now , `angleABC=180^(@)-(angleBAC+angleACB)=180^(@)-(25^(@)+90^(@))=180^(@)-115^(@)=65^(@)`
Again , ABCD is a cyclic quaadrilateral,
`thereforeangleADC+angleABC=180^(@)`
or, `angleADC+65^(@)=180^(@)"or",angle=180^(@)-65^(@)=115^(@)`
Also AB||DC and AC is their transversal, ltBRgt `thereforeangleACD="alternate"angleBAC=25^(@)`
`thereforeangleDAC=180^(@)-(angleADC+angleACD)`
`=180^(@)-(115^(@)+25^(@))=180^(@)-140^(@)=40^(@)`
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