Question

Determine the measure of an interior angle of a regular 15-gon.

A)2,340°


B)156°


C)180°


D)2,700°

Answer 1

The measure of an interior angle of a regular 15-gon is 156°.

Explanation:

To determine the measure of an interior angle of a regular 15-gon, we can use the formula:

Interior angle = (n-2) * 180° / n

where n represents the number of sides of the polygon.

For a regular 15-gon, n = 15. Plugging this value into the formula, we get:

Interior angle = (15-2) * 180° / 15

= 13 * 180° / 15

= 2340° / 15

= 156°

Answer 2

B) 156°

Explanation:

To find the measure of an interior angle of a regular polygon, we can use the following formula:

`\boxed{\begin{array}{c}\underline{\textsf{Interior angle of a regular polygon}}\\\\\textsf{Interior Angle} = (180^(\circ) (n - 2))/(n)\\\\\textsf{where $n$ is the number of sides}\end{array}}`

For a regular 15-gon, the value of n is 15.

Therefore, substitute n = 15 into the interior angle formula:

`\begin{aligned}\textsf{Interior Angle}&= (180^(\circ) (15 - 2))/(15)\\\\&= (180^(\circ) (13))/(15)\\\\&= (2340^(\circ))/(15)\\\\&=156^(\circ)\end{aligned}`

So, each interior angle of a regular 15-gon measures 156°.