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In the given figure, AD divides angleBAC...

In the given figure, AD divides `angleBAC` in the ratio 1 : 3 and AD=DB. Determine the value of x.

Text Solution

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The correct Answer is:
x=90
`angleBAC=(180^(@)-108^(@))=72^(@)`.
`angleBAD:angleCAD=1:3`
`:.angleBAD=((1)/(4)xx72^(@))=18^(@),angleCAD=((3)/(4)xx72^(@))=54^(@)`.
`AD=DBimpliesangleDBA=angleBAD=18^(@)`
`angleA+angleB+angleC=180^(@)implies72^(@)+18^(@)+x^(@)=180^(@)impliesx=90^(@)`.
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