Question

find the measure of angle 7.

Explanation:

Step1: Find the value of \(x\)

Since \(-9x + 171\) and \(6x+39\) are vertical angles, they are equal.
So, \(-9x + 171=6x + 39\).
Add \(9x\) to both sides: \(171=6x + 39+9x\), which simplifies to \(171 = 15x+39\).
Subtract \(39\) from both sides: \(171-39=15x\), so \(132 = 15x\).
Divide both sides by \(15\): \(x=\frac{132}{15}=\frac{44}{5} = 8.8\).

Step2: Find the measure of \(\angle6\)

Substitute \(x = 8.8\) into \(6x+39\): \(6\times8.8+39=52.8+39 = 91.8\).

Step3: Find the measure of \(\angle7\)

Since \(\angle6\) and \(\angle7\) are supplementary (they form a linear - pair), \(\angle6+\angle7 = 180^{\circ}\).
So, \(\angle7=180^{\circ}-\angle6\).
Substitute \(\angle6 = 91.8^{\circ}\): \(\angle7=180 - 91.8=88.2^{\circ}\).

Answer:

\(88.2^{\circ}\)