Question

Find the measures of an exterior angle and an interior angle given the number of sides of each regular polygon.

Round to the nearest tenth, if necessary.

Answer 1

`\theta = 25.7^\circ` --- Measure of each exterior angle

`\theta = 154.3^\circ` --- Measure of each interior angle

Explanation:

Given [Missing from the question]

`n = 14` --- 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:

`\theta = (360)/(n)`

Substitute 14 for n

`\theta = (360)/(14)`

`\theta = 25.7^\circ`

For an n-sided polygon, the measure of each interior angle is:

`\theta = ((n - 2) * 180)/(n)`

Substitute 14 for n

`\theta = ((14 - 2) * 180)/(14)`

`\theta = (12 * 180)/(14)`

`\theta = (2160)/(14)`

`\theta = 154.3^\circ`