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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