Question

a 10-sided equilateral polygon is drawn. Investigate and identify a pattern to find the angle measure of one interior angle

180
72
144
36

Answer 1

To find the measure of one interior angle of a regular polygon, you can use the formula for the measure of each interior angle of a regular \( n \)-sided polygon:

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

For a 10-sided polygon (decagon), \( n = 10 \):

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

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