Question

algebra the expressions $(9x + 5)^{circ}$ and $(11x - 25)^{circ}$ represent the measures of two angles of a regular nonagon. find the measure of an angle of the nonagon.

measure of an angle of the nonagon = $\square$ $^{circ}$

Explanation:

Step1: Recall regular polygon angles

In a regular polygon, all interior angles are equal. So, the two given angle expressions should be equal. Thus, we set up the equation: \(9x + 5 = 11x - 25\).

Step2: Solve for \(x\)

Subtract \(9x\) from both sides: \(5 = 2x - 25\).
Add 25 to both sides: \(30 = 2x\).
Divide by 2: \(x = 15\).

Step3: Find the angle measure

Substitute \(x = 15\) into one of the angle expressions, say \(9x + 5\):
\(9(15) + 5 = 135 + 5 = 140\).

Answer:

140