Question

a suppose the figure is a regular polygon. what is the measure of each exterior angle? c what is the sum of the exterior angles of the figure? b suppose the figure is a regular polygon. use the formula to calculate each interior angle measure.

Explanation:

Step1: Recall exterior - angle sum property

The sum of the exterior angles of any polygon, whether regular or irregular, is always $360^{\circ}$.
So, for a regular polygon, the sum of the exterior angles is $360^{\circ}$.

Step2: Find measure of each exterior angle

For a regular polygon with $n$ sides, the measure of each exterior angle $\theta$ is given by the formula $\theta=\frac{360^{\circ}}{n}$. But since we are not given the number of sides $n$ in the problem - statement for the measure of each exterior - angle part, if we assume the general case of a regular polygon, the sum of exterior angles is used as a fundamental property.

Answer:

c. The sum of the exterior angles of the figure (a regular polygon) is $360^{\circ}$.
d. Without knowing the number of sides $n$ of the regular polygon, we can only state the formula for the measure of each exterior angle as $\frac{360^{\circ}}{n}$. If we assume we are just stating the general result based on the property of exterior angles of a regular polygon, we can't give a numerical value for the measure of each exterior angle from the information given. But the formula is $\frac{360^{\circ}}{n}$, where $n$ is the number of sides of the regular polygon.