Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Ask your questions and receive precise answers from experienced professionals across different disciplines. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

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

Sagot :

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