# If the individual measure of an angle in a regular polygon is 156° how many sides does the polygon have?

Jun 8, 2018

$15$

#### Explanation:

The sum of the internal angles of a polygon with $n$ sides is $\left(n - 2\right) \cdot 180$ degrees.

If the polygon is regular, all the angles have the same measure, which means that each angle is

$\setminus \frac{\left(n - 2\right) \cdot 180}{n}$ degrees.

We know that this equals $156$, so we have

$\setminus \frac{\left(n - 2\right) \cdot 180}{n} = 156$

Multiply both sides by $n$:

$\left(n - 2\right) \cdot 180 = 180 n - 360 = 156 n$

Subtract $156 n$ from and add $360$ to both sides

$180 n - 156 n = 24 n = 360$

Divide both sides by $24$:

$n = \setminus \frac{360}{24} = 15$

Jun 8, 2018

$15$ sides

#### Explanation:

The sum of the exterior angles of any polygon is always 360°.

You can calculate the number of sides from (360°)/("ext angle")

Ext angle = 180°-156° = 24°

$\frac{360}{24} = 15$ sides