Question

find the measure of ∠npo. m∠npo = °

Explanation:

Step1: Use the property of alternate interior angles

Since \(LK\parallel NM\), \(\angle LOP=(75 - 3x)^{\circ}\) and \(\angle MPJ=(61 - x)^{\circ}\) are alternate interior angles. Also, \(\angle LOP\) and \(\angle MPJ\) are vertical angles. So \(75-3x = 61 - x\).

$$\begin{align*} 75-3x&=61 - x\\ -3x+x&=61 - 75\\ -2x&=-14\\ x& = 7 \end{align*}$$

Step2: Calculate \(\angle NPO\)

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

Answer:

\(54\)