What is the measure of one interior angle in a regular hexagon?
A regular hexagon is a polygon with six equal sides and measures of all interior angles are equal.
Answer: The measure of one interior angle in a regular hexagon is 120º.
Let's solve step by step.
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