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

Question

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°.