Question

the measure of an interior angle of a regular polygon is given find the number of sides in the polygon 175

Answer 1

72 sides

Step-by-step explanation:

The interior angle of a regular polygon can be calculated using the following equation:

`\text{Interior Angle = 180 - }(360)/(n)`

Where n is the number of sides of the polygon. If we replace the interior angle by 175 and we solve for n, we get:

`\begin{gathered} 175=180-(360)/(n) \\ (360)/(n)=180-175 \\ (360)/(n)=5 \\ 360=5n \\ (360)/(5)=n \\ 72=n \end{gathered}`

Therefore, a regular polygon with an interior angle of 175° has 72 sides.