To find the measure of every interior angle of a regular hexagon, first, we need to find the sum of the internal angles of a hexagon.
1. To find that, we need to use the following formula:
[tex]\text{ Sum of Interior angles of a polygon}=180(n-2)[/tex]Where n is the number of sides of a polygon. Since a hexagon has 6 sides, then n = 6, and we have:
[tex]180(6-2)=180(4)=720^{\circ}[/tex]Then the sum of the interior angles of a hexagon is 720 degrees.
2. Now, to find the measure of each interior angle of a regular hexagon, we need to apply the next formula:
[tex]\text{ Each interior angle of a regular polygon=}\frac{180(n-2)}{n}[/tex]And then, for n = 6 (regular hexagon), we have:
[tex]\frac{720^{\circ}}{6}=120^{\circ}[/tex]Therefore, in summary, the measure of every interior angle of a regular hexagon is 120° (120 degrees).
