Question

the measure of an interior angel of a regular polygon is 150. find the number of sides in the polygon.

Answer 1

The polygon has
`12` sides.

Explanation:

Recall that the expression for finding the measure of one interior angle of a regular polygon is
`(180(n-2))/(n)`, where
`n` is the number of sides the polygon has (and
`n\\eq 0`), which is what we want to find.

Because the measure of one interior angle of the given polygon is
`150\textdegree`, we can write the following equation to solve for
`n`:

`(180(n-2))/(n)=150`

Solving for
`n`, we get:

`(180(n-2))/(n)=150`

`(180n-360)/(n)=150` (Distribute the
`180` in the numerator)

`180n-360=150n` (Multiply both sides of the equation by
`n` to eliminate the denominator and simplify)

`30n-360=0` (Subtract
`150n` from both sides of the equation and simplify)

`30n=360` (Add
`360` to both sides of the equation to isolate
`n` and simplify)

`\bf n=12` (Divide both sides of the equation by
`30` to get rid of
`n`'s coefficient and simplify)

Therefore, the polygon has
`\bf 12` sides. Hope this helps!