Question

A 10-sided equilateral polygon is drawn. Investigate and identify a pattern to find the angle measure of one interior angle.(1 point)
Responses

72°
72°

180°
180°

36°
36°

144°

Answer 1

To find the measure of one interior angle of a regular 10-sided polygon (decagon), we can use the formula for the interior angle of a regular polygon:

\[
\text{Interior Angle} = \frac{(n - 2) \times 180°}{n}
\]

where \(n\) is the number of sides.

In this case, for a decagon:

\[
n = 10
\]

Plugging in the value:

\[
\text{Interior Angle} = \frac{(10 - 2) \times 180°}{10}
\]
\[
\text{Interior Angle} = \frac{8 \times 180°}{10}
\]
\[
\text{Interior Angle} = \frac{1440°}{10}
\]
\[
\text{Interior Angle} = 144°
\]

Thus, the measure of one interior angle of a regular 10-sided polygon is **144°**.