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In the figure, chords AC and DE intersec...

In the figure, chords AC and DE intersect at B. If `/_ABE = 108^(@)`, m (arc AE ) `= 95^(@)`, find m (arc DC).

Text Solution

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The correct Answer is:
`121^(@)`
`/_ABE=108^(@),m(arc AE)=95^(@)" ""…….."(" Given ")`
`/_ABE` has its vertex inside the circle and intercepts are AE and its vertically opposite `/_DBC` intercepts arc DC.
`/_ABE=(1)/(2)`[m (arc AE)+m(arc DC)]
`:.108^(@)=(1)/(2)xx[95^(@)+(arc DC)]`
`:.108^(@)xx2=95^(@)+m(arc DC)`
`:.216^(@)=95^(@)+m(arc DC)`
`:.m(arc DC)=216^(@)-95^(@)`
`:. m(arc DC)=121^(@)`
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