Question

1. solve for x. find the measures of the angles.

(3x + 16)°
(5x - 54)°

Explanation:

Step1: Set up the equation

Since the two angles are equal (assuming they are vertical - angles or corresponding - angles based on the parallel - line context), we set \(3x + 16=5x-54\).

Step2: Isolate the variable terms

Subtract \(3x\) from both sides: \(3x + 16-3x=5x-54 - 3x\), which simplifies to \(16 = 2x-54\).

Step3: Solve for \(x\)

Add 54 to both sides: \(16 + 54=2x-54 + 54\), so \(70 = 2x\). Then divide both sides by 2: \(x=\frac{70}{2}=35\).

Step4: Find the measure of the angles

Substitute \(x = 35\) into \(3x + 16\): \(3\times35+16=105 + 16=121\). Or substitute into \(5x-54\): \(5\times35-54=175-54 = 121\).

Answer:

\(x = 35\), and the measure of each angle is \(121^{\circ}\)