Question

If the measure of each interior angle of a regular polygon is 171, what is the number of sides in the polygon?

Answer 1

The polygon will have 40 sides.

Explanation:

The measure of the interior angles of a polygon is determined by the formula

`((n - 2)180)/n` = interior angle measure

were `n` is the number of angles and sides of the polygon.

We know that the interior angles of the polygon in the question have measures of `171^o`

`((n - 2)180)/n = 171^o`
`((n - 2)180) = 171^o(n)`
`180n - 360 = 171n`
`-360 = 171n-180n`
`-360 = -9n`
`-360/-9 = n`
`40 = n`

The polygon will have 40 sides.

Answer 2

Use the exterior angle to find there are `40` sides

Explanation:

The interior angle and the exterior angle of a polygon are adjacent supplementary angles. This means that they add to `180°`

Each exterior angle `= 180°-171° = 9°`

The sum of the exterior angles of any polygon is `360°`

`"Number of sides" = (360°)/"exterior angle"`

`"Number of sides" = (360°)/(9°) = 40` .