Question

find the measure of \\( \angle jno \\).
\\( m \angle jno= \\) \\( \circ \\)

Explanation:

Step1: Use the property of vertical angles

Since \( JK\parallel LM\), \(\angle JNO\) and \(\angle LOM\) are vertical - angles. Also, \(\angle JNO=(12x - 15)^{\circ}\) and \(\angle LOM=(5x + 48)^{\circ}\). By the property of parallel lines (corresponding angles are equal), we have \(12x-15 = 5x + 48\).

Step2: Solve the equation for \(x\)

Subtract \(5x\) from both sides of the equation \(12x-15 = 5x + 48\):
\(12x-5x-15=5x - 5x+48\), which simplifies to \(7x-15 = 48\).
Add \(15\) to both sides: \(7x-15 + 15=48 + 15\), so \(7x=63\).
Divide both sides by \(7\): \(x=\frac{63}{7}=9\).

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

Substitute \(x = 9\) into the expression for \(\angle JNO\).
\(\angle JNO=(12x - 15)^{\circ}\), so \(\angle JNO=(12\times9-15)^{\circ}\).
First, calculate \(12\times9 = 108\), then \(108-15=93\).

Answer:

\(93\)