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never [62]
2 years ago
6

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

Mathematics
1 answer:
zysi [14]2 years ago
5 0

<u>Given</u><u> </u><u>Information</u><u> </u><u>:</u><u>-</u>

⠀

  • Each exterior angle of a regular polygon has a measure of 40°

⠀

<u>To</u><u> </u><u>Find</u><u> </u><u>:</u><u>-</u>

⠀

  • The number of sides of the polygon

⠀

<u>Formula</u><u> </u><u>Used</u><u> </u><u>:</u><u>-</u>

⠀

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

⠀

<u>Solution</u><u> </u><u>:</u><u>-</u>

⠀

Using the formula,

⠀

\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

⠀

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

⠀

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

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