Question

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

Answer 1

22 sides

Explanation:

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

`((n-2)*180)/(n)`

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

`(360)/(n)`

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

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

`((n-2)*180)/(n)=10((360)/(n))`

Multiply both sides by "n":

`(n-2)*180=10n((360)/(n))`

Now, distribute:

`180(n)-180(2)=(3600n)/(n)\\180n-360=3600`

Divide both sides by 10:

`(180n)/(10)-(360)/(10)=(3600)/(10)\\`

`18n-36=360`

Add 36 to both sides:

`18n=360+36\\18n=396`

Divide both sides by 18:

`n=22`

The polygon has 22 sides