Question

Identify the measure of each exterior angle of a regular dodecagon

Answer 1

Given:

A dodecagon is a 12-sided polygon.

A regular dodecagon is a figure with sides of the same length and internal angles of the same size.

The sum of exterior angles of a polygon is 360°.

The formula for calculating the size of each exterior angle is;

`\begin{gathered} \text{Each exterior angle = }(360)/(n) \\ \text{where n is the number of sides of the polygon} \end{gathered}`

For a dodecagon, n = 12

Hence,

`\begin{gathered} \text{Each exterior angle = }(360)/(12) \\ \text{Each exterior angle = }30^0 \end{gathered}`

Therefore, each exterior angle of a regular dodecagon is 30 degrees.