Answer:
[tex]\theta = 25.7^\circ[/tex] --- Measure of each exterior angle
[tex]\theta = 154.3^\circ[/tex] --- Measure of each interior angle
Step-by-step explanation:
Given [Missing from the question]
[tex]n = 14[/tex] --- number of sides
Required
- The measure of an exterior angle
- The measure of an interior angle
For an n-sided polygon, the measure of each exterior angle is:
[tex]\theta = \frac{360}{n}[/tex]
Substitute 14 for n
[tex]\theta = \frac{360}{14}[/tex]
[tex]\theta = 25.7^\circ[/tex]
For an n-sided polygon, the measure of each interior angle is:
[tex]\theta = \frac{(n - 2) * 180}{n}[/tex]
Substitute 14 for n
[tex]\theta = \frac{(14 - 2) * 180}{14}[/tex]
[tex]\theta = \frac{12 * 180}{14}[/tex]
[tex]\theta = \frac{2160}{14}[/tex]
[tex]\theta = 154.3^\circ[/tex]
