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In the figure, m ) arc NS ) = 125^(@) ...

In the figure,
m ) arc NS ) `= 125^(@)`
m ( arc EF ) = `37^(@)`
find the measure `/_ NMS `,

Text Solution

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The correct Answer is:
`/_ NMS = 44^(@)`
m (arc NS ) `= 125^(@)` , m ( arc EF ) `= 37^(@)`
`/_ NMS ` has its vertex in the exterior of the circle and intercepts arc EF and arc NS.
`:. /_ NMS = (1)/(2) [ m (arc NS ) - m ( arc EF ) ]`
`:. /_ NMS = (1)/(2) xx [ 125 ^(@) - 37^(@)]`
`:. /_ NMS = (1)/(2) xx88^(@)` `:. /_ NMS = 44^(@)`
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