# The sum of the interior angles of a polygon is 4860 degrees. How many sides does the polygon have?

Mar 20, 2018

$29$

#### Explanation:

A polygon with $n$ sides can be dissected into $n - 2$ triangles with vertices at vertices of the polygon.

Each triangle contributes ${180}^{\circ}$ to the sum of the interior angles.

So with an interior angle sum of ${4860}^{\circ}$, the given polygon must have:

$\frac{4860}{180} + 2 = 27 + 2 = 29 \text{ }$ sides.