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Find the number of sides for a regular polygon whose interior angles each measure 10 times each exterior angle

Sagot :

Iciclepiano18idn

Answer:

22 sides

Step-by-step explanation:

The expression to find an interior angle of a polygon is:

[tex]\frac{(n-2)*180}{n}[/tex]

The expression to find an exterior angle of a polygon is:

[tex]\frac{360}{n}[/tex]

Please note that "n" represents the number of sides the polygon has.

We can use these two expressions to set up an equation.

[tex]\frac{(n-2)*180}{n}=10(\frac{360}{n})[/tex]

Multiply both sides by "n":

[tex](n-2)*180=10n(\frac{360}{n})[/tex]

Now, distribute:

[tex]180(n)-180(2)=\frac{3600n}{n}\\180n-360=3600[/tex]

Divide both sides by 10:

[tex]\frac{180n}{10}-\frac{360}{10}=\frac{3600}{10}\\[/tex]

[tex]18n-36=360[/tex]

Add 36 to both sides:

[tex]18n=360+36\\18n=396[/tex]

Divide both sides by 18:

[tex]n=22[/tex]

The polygon has 22 sides

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