Question

What is the measure of every interior angle of a regular hexagon?

Answer 1

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:

`\text{ Sum of Interior angles of a polygon}=180(n-2)`

Where n is the number of sides of a polygon. Since a hexagon has 6 sides, then n = 6, and we have:

`180(6-2)=180(4)=720^(\circ)`

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:

`\text{ Each interior angle of a regular polygon=}(180(n-2))/(n)`

And then, for n = 6 (regular hexagon), we have:

`(720^(\circ))/(6)=120^(\circ)`

Therefore, in summary, the measure of every interior angle of a regular hexagon is 120° (120 degrees).