Question

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

Answer 1

Answer:

The polygon has 15 sides

Step-by-step 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

$\displaystyle \frac{180(n-2)}{n}$

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

$\displaystyle \frac{180(n-2)}{n}=156$

Multiply by n:

$180(n-2)=156n$

Operate:

$180n-360=156n$

Reducing:

$24n=360$

Solving:

$n=15$

The polygon has 15 sides