Question

find the measures of an interior angle and an exterior angle of a regular hexagon.
the measure of an interior angle is \boxed{}.

Explanation:

Step1: Recall formula for interior angle

For a regular polygon with \( n \) sides, the measure of each interior angle is given by \( \frac{(n - 2)\times180^{\circ}}{n} \). A hexagon has \( n = 6 \) sides.

Step2: Substitute \( n = 6 \) into the formula

Substitute \( n = 6 \) into \( \frac{(n - 2)\times180^{\circ}}{n} \):
\( \frac{(6 - 2)\times180^{\circ}}{6}=\frac{4\times180^{\circ}}{6} \)
Simplify: \( \frac{720^{\circ}}{6}=120^{\circ} \).

Answer:

\( 120^{\circ} \)