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

To determine the measure of an interior angle of a regular hexagon, one can use the formula for calculating the measure of an interior angle of a regular polygon. The formula is:

[ \text{Interior Angle} = \frac{(n - 2) \times 180}{n}

]

where ( n ) is the number of sides of the polygon. For a hexagon, ( n = 6 ).

Substituting in the values for a hexagon:

[ \text{Interior Angle} = \frac{(6 - 2) \times 180}{6} = \frac{4 \times 180}{6} = \frac{720}{6} = 120 \text{ degrees} ]

Thus, the measure of an interior angle of a regular hexagon is 120 degrees. This result derives from the understanding that a hexagon consists of six equal angles, all measuring the same due to the regularity of the shape. Each interior angle contributes to the total of interior angles in the polygon, reinforcing the calculation.