What is the measure of each interior angle in a regular hexagon?A) 60 degreesB) 90 degreesC) 120 degreesD) 150 degrees

Break Down the Problem

1. Identify the number of sides in a regular hexagon, which is 6.
2. Determine the total sum of the interior angles of the hexagon.
3. Calculate the measure of each interior angle by dividing the total sum by the number of sides.

Relevant Concepts

1. The formula for the sum of the interior angles of a polygon with $n$ sides is given by: $\text{Sum of interior angles} = (n - 2) \times 180^\circ$

Analysis and Detail

1. For a hexagon ($n = 6$): $\text{Sum of interior angles} = (6 - 2) \times 180^\circ = 4 \times 180^\circ = 720^\circ$
2. Each interior angle in a regular hexagon can be found by dividing the total sum by the number of angles (which is equal to the number of sides): $\text{Each interior angle} = \frac{720^\circ}{6} = 120^\circ$

Verify and Summarize

The calculation confirms that each interior angle measures $120^\circ$.

Final Answer

The measure of each interior angle in a regular hexagon is C) 120 degrees.