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To find the angle measure of one interior angle of a regular polygon, we can use the formula:
\[
\text{Interior Angle} = \frac{(n - 2) \times 180^\circ}{n}
\]
where \( n \) is the number of sides of the polygon.
For a 10-sided polygon (decagon), we have \( n = 10 \). Plugging this value into the formula gives:
\[
\text{Interior Angle} = \frac{(10 - 2) \times 180^\circ}{10}
\]
Calculating the expression inside the parentheses:
\[
10 - 2 = 8
\]
Now multiplying by 180°:
\[
8 \times 180^\circ = 1440^\circ
\]
Now, divide by \( n = 10 \):
\[
\text{Interior Angle} = \frac{1440^\circ}{10} = 144^\circ
\]
Therefore, the measure of one interior angle of a regular 10-sided polygon is:
\[
\boxed{144^\circ}
\]