Question

the parallel lines x and y are cut by transversal z. the measures of two angles formed are given in the diagram. what is the measurement of the angle labeled (5x)°? 25° 55° 110° 125°

Explanation:

Step1: Use the property of parallel lines and transversal

When two parallel lines are cut by a transversal, the sum of an interior angle and its corresponding adjacent angle (on the same side of the transversal) is \(180^{\circ}\). Here, \(5x + 55=180\).

Step2: Solve the equation for \(x\)

Subtract \(55\) from both sides of the equation \(5x + 55=180\). We get \(5x=180 - 55\), so \(5x = 125\). Then divide both sides by \(5\), \(x=\frac{125}{5}=25\).

Step3: Calculate the measure of \(5x\)

Substitute \(x = 25\) into \(5x\). So \(5x=5\times25 = 125\).

Answer:

\(125^{\circ}\)