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In the adjoining figure, three coplanar ...

In the adjoining figure, three coplanar lines AB, CD and EF intersect at a point O. Find the value of x. Hence, find `angleAOD, angleCOE` and `angleAOE`.

Text Solution

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The correct Answer is:
`x=18, angleAOD=36^(@), angleCOE=90^(@), angleAOE=54^(@)`
`angleDOF=angleEOC=(5x)^(@)` [vertically opposite `angles`]
Now, EOF is a line. Sum of all angles above it is `180^(@)`.
`3x+5x+2x=180 implies 10x =180 implies x=18`.
`:. angleBOF=(3xx18)^(@)=54^(@), angleDOF=angleEOC=(5xx18)^(@)=90^(@), angleAOD=(2xx18)^(@)=36^(@)`.
`angleAOE=angleBOF=54^(@), angleCOE=angleDOF=90^(@)`.
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