Question

For each polygon, find (a) the interior angle sum and (b) the exterior angle sum.

Octagon.

Short answer

1. The interior angle sum for Octagon is $1080°$.
2. The exterior angle sum for Octagon is $360°$.

Step-by-step solution

Part a. 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 $\left(n-2\right)180$.

Part a. Step 2. Find the value of n.

The number of sides in a Octagon is 8.

Therefore, the value of$n$ is 8.

Part a. Step 3. Find the value of the interior angle sum of the Octagon.

By using the theorem for the sum of interior angles for convex polygon, the sum of the interior angles for the polygon having 8 sides is given by:

$$\begin{gathered} \left(8-2\right)180=6\times 180 \\ =1080 \end{gathered}$$

Therefore, the sum of interior angles for the Octagon is $1080°$.

Part b. Step 1. 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 $360°$.

Part b. Step 2. Find the value of n.

The number of sides in a Octagon is 8.

Therefore, the value of$n$ is 8.

Part b. Step 3. Find the value of the exterior angle sum of the Octagon.

By using the theorem for the sum of exterior angles for convex polygon, the sum of the exterior angles for the polygon having 8 sides is $360°$.

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