What is the measure of one interior angle in a regular hexagon?

Solution: 

A regular hexagon is a polygon with six equal sides and measures of all interior angles are equal.

The sum of exterior angles of a polygon is 360º.  

Let X be an exterior angle.

As we know that there are six exterior angles in a hexagon that is 6 X.

⇒ 6 X = 360º 

Therefore, every exterior angle measures 360º / 6 = 60º.

Now, as we can see in the figure the interior and exterior angles of the hexagon are in a straight line, that is, they form a pair of supplementary angles.

Let Y be an interior angle in the hexagon.

⇒ X + Y = 180º.

⇒ 60º + Y = 180º

⇒ Y = 120º

Thus, the measure of one interior angle in a regular hexagon is 120º.

What is the measure of one interior angle in a regular hexagon?

Summary:

The measure of one interior angle in a regular hexagon is 120º.