Given Information :-
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- Each exterior angle of a regular polygon has a measure of 40°
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To Find :-
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- The number of sides of the polygon
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Formula Used :-
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[tex] \qquad \star \: \underline{ \boxed{ \green{ \sf No.~of~sides = \dfrac{360^ \circ}{exterior ~angle}}}} \: \star[/tex]
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Solution :-
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Using the formula,
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[tex] \sf \dashrightarrow No. ~of~sides= \dfrac{360}{40} \\ \\ \\ \sf \dashrightarrow No. ~of~sides= \frac{ \cancel{360}}{ \cancel{40} } \\ \\ \\ \sf \dashrightarrow No. ~of~sides= \underline{ \boxed{ \blue { \frak{9}}}} \: \star[/tex]
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Thus, the polygon is a nonagon, and hence has 9 sides.
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[tex] \underline{\rule{227pt}{2pt}} \\ \\ [/tex]
