Question

solve for x.
$x = \square$
submit

Explanation:

Step1: Find the supplementary angle

The angle adjacent to \(125^{\circ}\) is \(180^{\circ}- 125^{\circ}=55^{\circ}\) (supplementary angles sum to \(180^{\circ}\)).

Step2: Use the property of parallel lines

Since \(LM\parallel NO\), the angle \(55^{\circ}\) and \((13x - 5)^{\circ}\) are congruent (corresponding angles). So \(13x-5 = 55\).

Step3: Solve the equation

Add \(5\) to both sides: \(13x=55 + 5=60\). Then divide both sides by \(13\): \(x=\frac{60}{13}\approx 4.615\) (This is wrong, actually, we made a mistake in step 1. The angle \(125^{\circ}\) and \((13x - 5)^{\circ}\) are same - side exterior and interior angles. Wait, no, correct way: The angle \(125^{\circ}\) and \((13x - 5)^{\circ}\) are supplementary because \(LM\parallel NO\) (same - side interior angles). So \(13x-5+125 = 180\).

Step4: Solve the correct equation

Simplify the left - hand side: \(13x+120 = 180\). Subtract \(120\) from both sides: \(13x=180 - 120=60\). Then \(x = 10\).

Answer:

\(x = 10\)