Question

One exterior angle of a regular polygon measures 10°. What is the measure of each interior angle? How many sides does the polygon have?

Answer 1

The interior angles of the regular polygon would each have a measure of `170^o`
The polygon would have 36 sides.

Explanation:

The interior and exterior angles of a polygon form a linear pair and are therefore supplementary with a sum of `180^o`?

If the exterior angle of polygon is `10^o` then the interior angle must be `170^o`.

In order to find the value of the interior angle of a regular polygon the equation is `((n-2)180)/n` where n is the number of sides of the regular polygon.

Given that the interior angle is `170^o` we can plug in the value into the formula
`170 = ((n-2)180)/n`
`170n = 180n-360`
`-10n = -360`
`n = 36`
Therefore the polygon has 36 sides.