Question

1. identify each missing angle measure. vertical (65x - 12)° (43x + 10)°

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. So, we set up the equation \(65x - 12=43x + 10\).

Step2: Solve for \(x\)

Subtract \(43x\) from both sides: \(65x-43x - 12=43x-43x + 10\), which simplifies to \(22x-12 = 10\). Then add 12 to both sides: \(22x-12 + 12=10 + 12\), getting \(22x=22\). Divide both sides by 22: \(x = 1\).

Step3: Find the angle measure

Substitute \(x = 1\) into either expression for the angle. Using \(65x-12\), we have \(65\times1-12=53^{\circ}\).

Answer:

\(53^{\circ}\)