Question

Find the measure of one interior angle in each regular polygon. Round your answer to the nearest tenth if necessary.

regular 17-gon

Question 14 options:

161.1


158.8


152.3


150

Answer 1

To find the measure of one 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 (or vertices) of the polygon.

For a regular 17-gon, \( n = 17 \):

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

Calculating step by step:

1. Calculate \( n - 2 \):
\[
17 - 2 = 15
\]

2. Multiply by 180:
\[
15 \times 180 = 2700
\]

3. Divide by \( n \):
\[
\frac{2700}{17} \approx 158.823529
\]

Rounding to the nearest tenth, we get:

\[
158.8
\]

Therefore, the measure of one interior angle in a regular 17-gon is **158.8**.