What is the measure of an interior angle in a regular polygon with 17 sides?

Question

Write your answer as an integer or as a decimal rounded to the nearest tenth.

Answer 1

To find the measure of an interior angle in 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 regular polygon with 17 sides, we can substitute \( n = 17 \) into the formula:

\[ \text{Interior angle} = \frac{(17-2) \times 180}{17} \]

Calculating this step by step:

1. Calculate \( 17 - 2 = 15 \).
2. Multiply by 180: \( 15 \times 180 = 2700 \).
3. Divide by 17:

\[ \frac{2700}{17} \approx 158.8235294117647 \]

Rounding this to the nearest tenth yields \( 158.8 \).

Therefore, the measure of an interior angle in a regular polygon with 17 sides is approximately:

\[ \boxed{158.8} \]