A regular $22$-gon is a polygon with $22$ equal sides and angles. What is the measure of each interior angle of a regular $22$-gon? If necessary, round your answer to the nearest tenth. (Use the formula for each interior angle: $\frac{(n-2)\times 180}{n}$ where $n$ is the number of sides.)

• A. $140.0°$
• B. $147.3°$
• C. $170.5°$
• D. $163.6°$

Answer: (D)

Verified step by step guidance

1. Identify the number of sides of the regular polygon, which is given as \(n = 22\).
2. Recall the formula for the measure of each interior angle of a regular polygon: \(\text{Interior Angle} = \frac{(n - 2) \times 180}{n}\)
3. Substitute \(n = 22\) into the formula: \(\text{Interior Angle} = \frac{(22 - 2) \times 180}{22}\)
4. Simplify the numerator by calculating \((22 - 2) = 20\), so the expression becomes: \(\text{Interior Angle} = \frac{20 \times 180}{22}\)
5. Calculate the fraction and multiply to find the measure of each interior angle, then round the result to the nearest tenth if necessary.