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In the adjoining figure, ABCD is a cycli...

In the adjoining figure, `ABCD` is a cyclic quadrilateral whose side `AB` is the diameter of the circle . If `angle ADC=140^(@)` , then find the value of `angleBAC`.

Text Solution

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Since, `ABCD` is a cyclic quadrilateral .
`thereforeangle ADC+angle ABC=180^@`
`rArr140^@+angle ABC=180^@`
`rArrangle ABC=180^@-140^@`
`rArrangle ABC =40^@`
`AB` is the diameter of circle.

`thereforeangleACB=90^@` (angle in a semi- circle)
Now, in `Delta ABC`
` angle BAC=angle ABC+anlge ACB=180^@`
`rArrangle BAC +40^@+90^@=180^@`
`rArrangle BAC =180^@-130^@`
`rArrangle BAC -50^@`
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