Question

Determine the sum of the measures of the interior angles of a dodecagon (12-sided polygon).

A)540°


B)1,800°


C)2,160°


D)360°

Answer 1

B) 1800°

Explanation:

To determine the sum of the measures of the interior angles of a dodecagon (12-sided polygon), we can use the following formula:

`\boxed{\begin{array}{c}\underline{\textsf{Sum of the interior angles of a polygon}}\\\\\textsf{Sum} = 180^(\circ) (n - 2)\\\\\textsf{where $n$ is the number of sides}\end{array}}`

Substitute n = 12 into the formula:

`\begin{aligned}\textsf{Sum}&= 180^(\circ) (12 - 2)\\\\&=180^(\circ) (10)\\\\&=1800^(\circ)\end{aligned}`

Therefore, the sum of the measures of the interior angles of a dodecagon is 1800°.