Question

THE INTERIOR ANGLE OF A REGULAR POLYGON IS 170° FIND THE NUMBER OF SIDES.​

Answer 1

Correct Question-:

• The interior angle of a regular polygon is 170º. Find the number of sides of the polygon.

AnswEr-:

• $\underline{\boxed{\star{\sf{\blue{  The\:number \;of\:sides\:of\:Regular\:polygon\:= 36\: Sides.}}}}}$

EXPLANATION-:

• $\frak{Given \:\: -:} \begin{cases} \sf{ The \:interior\: angle\: of \:a\: regular \:polygon \:is\: .\:=\:\frak{170 ^{⁰} }}\end{cases}$

• $\frak{To \:Find\: -:} \begin{cases} \sf{ The \:number\: \: of \:a\:sides\:of\: regular \:polygon \:\: .\:}\end{cases}$

Solution-:

• $\underline{\boxed{\star{\sf{\blue{  Formula\:applied\:for\:Side\:of\:Regular \:Polygon \;\:= \frac{180^{⁰}(n -2)}{n} = one\:interior \:Angle.}}}}}$

• $\frak{Here \:\: -:} \begin{cases} \sf{ The \:interior\: angle\: of \:a\: regular \:polygon \:is\: .\:=\:\frak{170^{⁰}}}& \\\\ \sf{n \: = \frak{ Number \;of\:Sides}}\end{cases}$

Now ,

• Substituting the value -:

• $\implies{\sf{\large { \frac{180^{⁰}(n-2)}{n}= 170 ^{⁰} }}}$
• $\implies{\sf{\large { 180 ^{⁰} (n-2)= 170n }}}$ _______________[ Cross Multiplication]
• $\implies{\sf{\large { 180n-360= 170n }}}$
• $\implies{\sf{\large { 180n - 170n = 360 ^{⁰} }}}$
• $\implies{\sf{\large { 10n= 360^{⁰} }}}$
• $\implies{\sf{\large { n = \frac{360}{10} }}}$
• $\implies{\sf{\large { n = 36 }}}$

Therefore,

• $\underline{\boxed{\star{\sf{\blue{  n\: = 36.}}}}}$

Hence ,

• $\underline{\boxed{\star{\sf{\blue{  The\:number \;of\:sides\:of\:Regular\:polygon\:= 36\: Sides.}}}}}$

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