To calculate the sum of the interior angles of a polygon, we can use the formula:
\[ \text{Sum of Interior Angles} = (n - 2) \times 180^\circ \]
where \( n \) is the number of sides in the polygon.
a. Sum of the Interior Angles of a Regular Hexagon (6 sides)
- For a hexagon, \( n = 6 \).
- Substitute into the formula:
\[ \text{Sum of Interior Angles} = (6 - 2) \times 180^\circ = 4 \times 180^\circ = 720^\circ \]
The sum of the interior angles of a regular hexagon is 720 degrees.
b. Measure of One Interior Angle
To find the measure of one interior angle in a regular polygon, we use the formula:
\[ \text{Measure of One Interior Angle} = \frac{\text{Sum of Interior Angles}}{n} \]
- Using the sum calculated in part (a):
\[ \text{Measure of One Interior Angle} = \frac{720^\circ}{6} = 120^\circ \]
The measure of one interior angle of a regular hexagon is 120 degrees.