To determine the measure of each interior angle of a regular pentagon, follow these steps:
1. A regular [tex]\(n\)[/tex]-sided polygon has its interior angles equal. The formula for calculating the measure of each interior angle of a regular [tex]\(n\)[/tex]-sided polygon is:
[tex]\[
\text{Interior angle} = \frac{(n-2) \times 180^\circ}{n}
\][/tex]
2. In this case, the polygon is a pentagon, which means it has [tex]\(n = 5\)[/tex] sides.
3. Substitute [tex]\(n = 5\)[/tex] into the formula:
[tex]\[
\text{Interior angle} = \frac{(5-2) \times 180^\circ}{5}
\][/tex]
4. Simplify the expression inside the parentheses:
[tex]\[
\text{Interior angle} = \frac{3 \times 180^\circ}{5}
\][/tex]
5. Multiply the values:
[tex]\[
\text{Interior angle} = \frac{540^\circ}{5}
\][/tex]
6. Divide the result:
[tex]\[
\text{Interior angle} = 108^\circ
\][/tex]
Thus, the measure of each interior angle of a regular pentagon is [tex]\(108^\circ\)[/tex]. Therefore, the answer is:
[tex]\[ \boxed{108^\circ} \][/tex]
