Question

1. if the figure below is a regular polygon, find the value of x.

(10x + 4)°

Explanation:

Step1: Determine the number of sides

The polygon in the figure is a nonagon (9 - sided polygon).

Step2: Recall the formula for interior angle of regular polygon

The formula for the measure of each interior angle of a regular polygon with \( n \) sides is \( \frac{(n - 2)\times180^{\circ}}{n} \). For \( n = 9 \), we have:
\[
\frac{(9 - 2)\times180^{\circ}}{9}=\frac{7\times180^{\circ}}{9}=140^{\circ}
\]

Step3: Set up the equation

We know that each interior angle is \( (10x + 4)^{\circ} \), so we set up the equation:
\[
10x + 4 = 140
\]

Step4: Solve for \( x \)

Subtract 4 from both sides:
\[
10x = 140 - 4 = 136
\]
Divide both sides by 10:
\[
x=\frac{136}{10}=13.6
\]

Answer:

\( x = 13.6 \)