Question

find the measure of \\( \angle jno \\).
\\( m \angle jno = \square ^ { \circ } \\)

Explanation:

Step1: Use the property of parallel lines and transversal (corresponding angles)

Since \( JK\parallel LM\), \(\angle JNO\) and \(\angle LOM\) are corresponding angles. Also, \(\angle LOM\) and \((5x + 48)^{\circ}\) are vertical angles. And \(\angle JNO=(12x-15)^{\circ}\). Because \(JK\parallel LM\), \(\angle JNO\) and \((5x + 48)^{\circ}\) are congruent (corresponding angles). So, \(12x-15 = 5x+48\).

Step2: Solve the equation for \(x\)

Subtract \(5x\) from both sides: \(12x-5x-15=5x - 5x+48\), which gives \(7x-15 = 48\).
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 \(12x-15\). Then \(12x-15=12\times9-15\).
First, calculate \(12\times9 = 108\). Then \(108-15=93\).

Answer:

\(93\)