Triangle Proofs Quick Check

Question

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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°

36°
36°

144°
144°

180°

Answer 1

To find the measure of one interior angle of a regular polygon, you can use the formula:

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

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

For a 10-sided polygon (decagon):

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

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

Therefore, the correct response is 144°.