Question

write an equation for the transversal. 5x + 50, 2x - 20

Explanation:

Step1: Identify Angle Relationship

The two angles formed by the transversal with the parallel lines are same - side interior angles? Wait, no, looking at the expressions \(5x + 50\) and \(2x-30\), actually, if the lines are parallel, and the angles are same - side interior angles, they should be supplementary. Wait, or maybe they are alternate exterior or something? Wait, no, the problem is to write an equation for the transversal. Wait, maybe the angles are supplementary (since they are on the same side of the transversal and between two parallel lines, so same - side interior angles sum to \(180^{\circ}\)). So the equation should be \((5x + 50)+(2x-30)=180\).

Step2: Simplify the Equation

Combine like terms: \(5x+2x + 50-30=180\), so \(7x + 20=180\). Then subtract 20 from both sides: \(7x=180 - 20=160\)? Wait, no, maybe I misidentified the angle relationship. Wait, maybe the angles are equal? If they are alternate interior angles, then \(5x + 50=2x-30\)? But that would give a negative \(x\), which is not possible. So more likely, they are same - side interior angles, so supplementary. So the equation is \(5x + 50+2x-30 = 180\), which simplifies to \(7x+20 = 180\), then \(7x=160\)? Wait, no, maybe the lines are parallel and the angles are supplementary. Let's re - check. The two angles: one is \(5x + 50\), the other is \(2x-30\). If the lines are parallel, same - side interior angles are supplementary. So the equation is \((5x + 50)+(2x-30)=180\).

Answer:

\(5x + 50+2x-30 = 180\) (or simplified as \(7x + 20=180\))