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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).

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