Question

find the value of x in the regular nonagon. (8x + 12)° x = (type an integer or a fraction.)

Explanation:

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

The formula for the measure of each interior angle of a regular \( n \)-sided polygon is \( \frac{(n - 2)\times180^{\circ}}{n} \). For a nonagon, \( n = 9 \).

Step2: Calculate the measure of each interior angle of a regular nonagon.

Substitute \( n = 9 \) into the formula:
\[
\frac{(9 - 2)\times180^{\circ}}{9}=\frac{7\times180^{\circ}}{9}= 140^{\circ}
\]

Step3: Set up the equation and solve for \( x \).

We know that the interior angle of the regular nonagon is \( (8x + 12)^{\circ} \), and we found it should be \( 140^{\circ} \). So we set up the equation:
\[
8x+12 = 140
\]
Subtract 12 from both sides:
\[
8x=140 - 12=128
\]
Divide both sides by 8:
\[
x=\frac{128}{8} = 16
\]

Answer:

\( 16 \)