Question

Each interior angle of a regular polygon has a measure of 40.how many sides does the polygon have?​

Answer 1

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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`\qquad \star \: \underline{ \boxed{ \green{ \sf No.~of~sides = (360^ \circ)/(exterior ~angle)}}} \: \star`

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Solution :-

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Using the formula,

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`\sf \dashrightarrow No. ~of~sides= (360)/(40) \\ \\ \\ \sf \dashrightarrow No. ~of~sides= \frac{ \cancel{360}}{ \cancel{40} } \\ \\ \\ \sf \dashrightarrow No. ~of~sides= \underline{ \boxed{ \blue { \frak{9}}}} \: \star`

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Thus, the polygon is a nonagon, and hence has 9 sides.

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`\underline{\rule{227pt}{2pt}} \\ \\`