Question

current skill $ find the measure of angle 2. 1 2 3 -9x - 52 7x + 220 6 7 8 label optional

Explanation:

Step1: Identify angle - pair relationship

Angles \(7x + 220\) and \(-9x-52\) are vertical angles, and vertical angles are equal. So we set up the equation \(7x + 220=-9x - 52\).

Step2: Solve the equation for \(x\)

Add \(9x\) to both sides: \(7x+9x + 220=-9x+9x - 52\), which simplifies to \(16x+220=- 52\). Then subtract 220 from both sides: \(16x+220 - 220=-52 - 220\), giving \(16x=-272\). Divide both sides by 16: \(x=\frac{-272}{16}=-17\).

Step3: Find the measure of angle 2

Substitute \(x = - 17\) into the expression for the angle adjacent to angle 2 (\(-9x - 52\)). First, calculate \(-9x-52=-9\times(-17)-52=153 - 52 = 101\). Angle 2 and the angle \(-9x - 52\) are supplementary (linear - pair, sum to \(180^{\circ}\)). Let the measure of angle 2 be \(y\), then \(y+(-9x - 52)=180\). Substituting the value of \(-9x - 52 = 101\), we get \(y=180 - 101 = 79\).

Answer:

\(79\)