calculate the measure of each interior angle of a regular decagon.
______ degrees
question 28 1 pts
calculate the measure for each interior angle of a regular 27 - gon.
152.04°
162.58°
174.21°
166.67°
none of these answers are correct.

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for the measure of an interior angle of a regular polygon
The formula for the measure of an interior angle $\theta$ of a regular $n -$sided polygon is $\theta=\frac{(n - 2)\times180^{\circ}}{n}$

## Step2: Calculate for a decagon ($n = 10$)
Substitute $n = 10$ into the formula:
$$
\begin{align*}
\theta&=\frac{(10 - 2)\times180^{\circ}}{10}\
&=\frac{8\times180^{\circ}}{10}\
&=144^{\circ}
\end{align*}
$$

## Step3: Calculate for a $27 -$gon ($n = 27$)
Substitute $n = 27$ into the formula:
$$
\begin{align*}
\theta&=\frac{(27- 2)\times180^{\circ}}{27}\
&=\frac{25\times180^{\circ}}{27}\
&=\frac{4500^{\circ}}{27}\
& = 166.\overline{6}^{\circ}\approx166.67^{\circ}
\end{align*}
$$

# Answer:
For the regular decagon: $144$
For question 28: $166.67^{\circ}$ (the fourth option $166.67^{\circ}$ is correct)

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for the measure of an interior angle of a regular polygon

Step2: Calculate for a decagon (\(n = 10\))

Step3: Calculate for a \(27 -\)gon (\(n = 27\))

Answer: