Question

If the measure of one interior angle of a regular polygon is 156° , how many sides does it have?

Answer 1

The polygon has 15 sides

Explanation:

Angles in a Regular Polygon

A polygon with n sides has a total sum of internal angles equal to 180°(n-2). This means that in a regular polygon, each angle measures

`\displaystyle (180(n-2))/(n)`

The regular polygon's interior angle is 156°, thus

`\displaystyle (180(n-2))/(n)=156`

Multiply by n:

`180(n-2)=156n`

Operate:

`180n-360=156n`

Reducing:

`24n=360`

Solving:

`n=15`

The polygon has 15 sides