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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$\qquad \star \: \underline{ \boxed{ \green{ \sf No.~of~sides = \dfrac{360^ \circ}{exterior ~angle}}}} \: \star$

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Solution :-

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Using the formula,

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$\sf \dashrightarrow No. ~of~sides= \dfrac{360}{40} \\ \\ \\ \sf \dashrightarrow No. ~of~sides= \frac{ \cancel{360}}{ \cancel{40} } \\ \\ \\ \sf \dashrightarrow No. ~of~sides= \underline{ \boxed{ \blue { \frak{9}}}} \: \star$

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

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