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:
\[ \boxed{144^\circ} \]
1 answer