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

To find the measure of each interior angle of a regular hexagon, one can use the formula for the interior angle of a regular polygon, which is given by:

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

]

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

Plugging in the value:

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

This calculation shows that each interior angle of a regular hexagon measures 120 degrees.

The reason this value makes sense is that a regular hexagon can be divided into 6 equilateral triangles, each having angles of 60 degrees. The interior angles at each vertex of the hexagon are formed by two of these triangles, leading to an angle of ( 60 + 60 = 120) degrees.

Thus, the correct answer indicates that each interior angle of a regular hexagon measures 120 degrees,