Question

solve for x. find m∠y. find m∠y

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. So, \(3x - 1=15x - 17\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(-1 = 15x-3x - 17\), which simplifies to \(-1=12x - 17\). Then add 17 to both sides: \(16 = 12x\). Divide both sides by 12: \(x=\frac{16}{12}=\frac{4}{3}\).

Step3: Find the measure of an angle adjacent to \(y\)

We know that the angle \(129^{\circ}\) and the angle adjacent to \(y\) are supplementary (sum to \(180^{\circ}\)). Let the adjacent - angle to \(y\) be \(a\), then \(a = 180 - 129=51^{\circ}\).

Step4: Find \(m\angle y\)

Since \(y\) and the \(51^{\circ}\) angle are vertical angles, \(m\angle y = 51^{\circ}\).

Answer:

\(m\angle y = 51^{\circ}\)