Question

find the measure of ∠npo. m∠npo = °

Explanation:

Step1: Use corresponding - angles property

Since the two lines are parallel, the corresponding angles are equal. So, \(61 - x=75 - 3x\).

Step2: Solve the equation for \(x\)

Add \(3x\) to both sides: \(61 - x+3x=75 - 3x+3x\), which simplifies to \(61 + 2x=75\). Then subtract 61 from both sides: \(2x=75 - 61\), so \(2x = 14\). Divide both sides by 2: \(x = 7\).

Step3: Find the measure of \(\angle NPO\)

Substitute \(x = 7\) into the expression for \(\angle NPO=(75 - 3x)^{\circ}\). Then \(75-3\times7=75 - 21=54^{\circ}\).

Answer:

\(54\)