Question

A polygon has 102 sides. What is the interior angle sum? The exterior angle sum?

Short answer

The interior angle sum of the polygon is and the exterior angle sum is .

Step-by-step solution

Step 1. Write the theorem for the sum of interior angles for convex polygon.

The theorem for the sum of interior angles for convex polygon states that the sum of measures of the interior angles of a convex polygon with sides is $\left(n-2\right)180$.

Step 2. Find the value of the interior angle sum of the polygon.

By using the theorem for the sum of interior angles for convex polygon, the sum of the interior angles for the polygon having 102 sides is given by:

$\begin{array}{c}\left(102-2\right)180=100\times 180\\ =18000\end{array}$

Therefore, the sum of interior angles for the polygon is $18000°$.

Step 3. Write the theorem for the sum of exterior angles for convex polygon.

The theorem for the sum of exterior angles for convex polygon states that the sum of measures of the exterior angles of a convex polygon is $360°$.

Step 4. Find the value of the exterior angle sum of the polygon.

By using the theorem for the sum of exterior angles for convex polygon, the sum of the exterior angles for the polygon having 102 sides is $360°$.

Therefore, the sum of exterior angles of the polygon is $360°$.