Question

Complete each statement with the word always, sometimes, or never.

As the number of sides of a regular polygon increases, the measure of each exterior angle$\underset{\mathbf{¯}}{\mathbf{?}}$ decreases.

Short answer

As the number of sides of a regular polygon increase, the measure of each exterior angle always decreases.

Step-by-step solution

Step 1. Write the formula for the measure of each exterior angle of a regular polygon.

The formula for the measure of each exterior angle of a regular polygon with sides is$\frac{\mathbf{360}}{\mathbf{n}}$

Step 2. Write the relationship between the value of a number of sides and the measure of each exterior angle of the polygon.

The measure of each exterior angle of a regular polygon with$n$ sides is $\frac{360}{n}$.

Therefore, it can be noticed that the measure of each exterior angle of a regular polygon is inversely proportional to the number of sides of the polygon.

Therefore, the relationship between the measure of each exterior angle of a regular polygon and the number of sides of the polygon is that both are inversely proportional to each other.

Step 3. Write the conclusion.

The measure of each exterior angle of a regular polygon is inversely proportional to the number of sides of the polygon.

Therefore, if the number of sides of a regular polygon increases, then the measure of each exterior angle of the polygon decreases.

Therefore, as the number of sides of a regular polygon increase, the measure of each exterior angle always decreases.