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

1 answer

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.

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