Question

A 10-sided equilateral polygon is drawn. Investigate and identify a pattern to find the angle measure of one interior angle
A. 144 degrees
B. 36 degrees
C. 180 degrees
D. 72 degrees

Answer 1

To find the measure of one interior angle of a regular polygon (in this case, a 10-sided equilateral polygon, known as a decagon), you can use the formula for the measure of an interior angle:

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

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

For a decagon, \( n = 10 \):

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

So the measure of one interior angle of a regular decagon is \( 144 \) degrees.

Thus, the correct answer is **A. 144 degrees**.