Question

1. l || m, find x

Explanation:

Step1: Find the angle adjacent to 73°

The sum of angles on a straight line is 180°. So the angle adjacent to 73° (let's call it \( y \)) is \( 180 - 73 = 107^\circ \)? Wait, no, wait. Wait, the 57° and the angle between the transversal and line \( m \) (other than 73°) – wait, actually, since \( l \parallel m \), we can use the concept of corresponding angles or alternate interior angles. Wait, first, let's find the angle that is supplementary to 73°? No, wait, the 57° and the angle formed by the transversal and the vertical line (the one with \( x \)) – wait, maybe we can use the fact that the sum of angles in a triangle or the consecutive interior angles? Wait, no, let's look again.

Wait, the two lines \( l \) and \( m \) are parallel, cut by a transversal and a vertical line. The angle of 57° and the angle adjacent to 73° (let's calculate that first). The angle next to 73° on line \( m \) (since it's a straight line) is \( 180 - 73 = 107^\circ \)? No, that can't be. Wait, maybe the 57° and the angle with \( x \) are related by the parallel lines. Wait, actually, the sum of 57°, 73°, and the angle supplementary to \( x \) should be 180°? Wait, no, let's think of the vertical line as a transversal. Wait, the angle \( x \) and the angle formed by the transversal (the slanted one) and the vertical line – since \( l \parallel m \), the sum of the angles 57°, 73°, and the angle that is supplementary to \( x \) should be 180°? Wait, no, maybe the angle \( x \) is equal to the sum of 57° and 73°? Wait, let's check: 57 + 73 = 130? No, wait, 57 + 73 = 130? Wait, 57 + 73 = 130? Wait, 50 + 70 = 120, 7 + 3 = 10, so 130. Wait, but why?

Wait, when two parallel lines are cut by a transversal, the consecutive interior angles are supplementary, but here we have a vertical line and a slanted transversal. Wait, actually, the angle \( x \) is an exterior angle or a corresponding angle. Wait, let's consider the triangle formed? No, maybe the angle \( x \) is equal to 57° + 73° because of the parallel lines and the transversal. Let's verify: 57 + 73 = 130. So \( x = 57 + 73 = 130^\circ \)? Wait, 57 + 73 = 130, yes. Because the two angles 57° and 73° are on the same side of the transversal, and since \( l \parallel m \), the angle \( x \) is equal to the sum of these two angles (alternate interior angles or corresponding angles concept). So:

Step1: Calculate the sum of 57° and 73°

\( 57^\circ + 73^\circ = 130^\circ \)

Step2: Determine \( x \)

Since \( l \parallel m \), the angle \( x \) is equal to the sum of 57° and 73° (by the property of parallel lines and transversals, the exterior angle or the corresponding angle). So \( x = 57 + 73 = 130^\circ \)

Answer:

\( \boxed{130^\circ} \)