Given in the question:
a.) The sum of all angles of a polygon is 1,440 degrees.
To be able to determine what polygon has a total sum of angles of 1,440 degrees, we will be using the following formula:
[tex]\text{ }\Theta=(n-2)x180^{\circ}[/tex]We get,
[tex]\text{ 1},440^{\circ}=(n-2)x180^{\circ}[/tex][tex]\text{ 1},440^{\circ}=180n-360^{\circ}[/tex][tex]180n=1,440^{\circ}\text{ + 360}^{\circ}[/tex][tex]180n=1,800^{\circ}[/tex][tex]\frac{180n}{180}=\frac{1,800^{\circ}}{180}[/tex][tex]n\text{ = 10}[/tex]Therefore, that polygon is a decagon or a polygon with 10 sides.
