Question

solve for x.
(there is a diagram with lines and angles: a transversal intersecting two parallel lines, with angle at p being 125° and angle at q being (13x - 5)°)
x = box
submit

Explanation:

Step1: Identify Parallel Lines and Angles

Lines \( LM \) and \( NO \) are parallel (since they have the same direction arrows), and \( JK \) is a transversal. The \( 125^\circ \) angle and \( (13x - 5)^\circ \) angle are corresponding angles (or alternate exterior/interior, but here they are equal because of parallel lines and transversal, so they should be equal as corresponding angles? Wait, actually, the \( 125^\circ \) and the angle at \( Q \) (the one with \( 13x - 5 \))—wait, no, actually, the \( 125^\circ \) and the angle adjacent to \( (13x - 5) \)? Wait, no, let's check: since \( LM \parallel NO \), the \( 125^\circ \) angle and \( (13x - 5)^\circ \) are equal because they are corresponding angles. Wait, actually, when two parallel lines are cut by a transversal, corresponding angles are equal. So \( 13x - 5 = 125 \)? Wait, no, wait: wait, the angle at \( P \) is \( 125^\circ \), and the angle at \( Q \) (the one labeled \( 13x - 5 \))—wait, maybe they are equal because \( LM \parallel NO \), so corresponding angles. So set \( 13x - 5 = 125 \).

Step2: Solve for \( x \)

Add 5 to both sides: \( 13x = 125 + 5 = 130 \). Then divide both sides by 13: \( x = \frac{130}{13} = 10 \).

Answer:

\( x = 10 \)