Question

6.1 polygons hw
find the measure of 1 exterior angle in the regular polygon.
1 exterior angle measure:

Explanation:

Step1: Recall the formula for the measure of an exterior angle of a regular polygon

The sum of the exterior angles of any polygon is \(360^{\circ}\). For a regular polygon with \(n\) sides, the measure of one exterior angle \(E\) is given by the formula \(E=\frac{360^{\circ}}{n}\).

Step2: Determine the number of sides \(n\)

The given polygon is a dodecagon (12 - sided polygon), so \(n = 12\).

Step3: Calculate the measure of one exterior angle

Substitute \(n=12\) into the formula \(E=\frac{360^{\circ}}{n}\).

$$E=\frac{360^{\circ}}{12}=30^{\circ}$$

Answer:

\(30^{\circ}\)