Question

3 numeric 0.5 points what is the measure of angle 1? type in your numerical answer only, no degree symbol.

Explanation:

Step1: Identify angle relationship

The two horizontal lines are parallel (since they are both straight and horizontal), and the vertical line is a transversal. The angle of \(78^\circ\) and angle 1 are corresponding angles (or alternate interior angles, depending on the configuration), but actually, looking at the diagram, the angle of \(78^\circ\) and angle 1 are equal? Wait, no, wait. Wait, actually, the two horizontal lines are parallel, and the vertical line is a transversal. Wait, no, maybe the angle of \(78^\circ\) and angle 1 are equal because the lines are parallel? Wait, no, maybe it's a case of vertical angles or corresponding angles. Wait, actually, the two horizontal lines are parallel, and the vertical line is a transversal, so the angle of \(78^\circ\) and angle 1 are equal? Wait, no, wait, maybe the angle of \(78^\circ\) and angle 1 are equal because the lines are parallel and the transversal creates corresponding angles. Wait, no, maybe I made a mistake. Wait, actually, the two horizontal lines are parallel, and the vertical line is a transversal, so the angle of \(78^\circ\) and angle 1 are equal. Wait, no, wait, maybe it's a case of alternate interior angles. Wait, no, let's think again. The angle of \(78^\circ\) and angle 1: since the two horizontal lines are parallel, and the vertical line is a transversal, the angle of \(78^\circ\) and angle 1 are equal. Wait, no, maybe not. Wait, maybe the angle of \(78^\circ\) and angle 1 are supplementary? No, that doesn't make sense. Wait, no, looking at the diagram, the two horizontal lines are parallel, and the vertical line is a transversal, so the angle of \(78^\circ\) and angle 1 are equal. Wait, no, maybe the angle of \(78^\circ\) and angle 1 are equal because they are corresponding angles. Wait, yes, because the two horizontal lines are parallel, and the vertical line is a transversal, so corresponding angles are equal. So angle 1 is equal to \(78^\circ\)? Wait, no, wait, maybe I got it wrong. Wait, no, the diagram shows two horizontal lines (parallel) and two vertical lines? Wait, no, the diagram has two horizontal lines (one above, one below) and two vertical lines? Wait, no, the diagram has two horizontal lines (each with two arrows) and two vertical lines (each with two arrows). Wait, the angle of \(78^\circ\) is between the upper vertical line and the upper horizontal line. Then angle 1 is between the lower vertical line and the lower horizontal line. Wait, no, maybe the two horizontal lines are parallel, and the two vertical lines are parallel? No, the vertical lines are the same line? Wait, no, the diagram shows two horizontal lines (each is a straight line with arrows on both ends) and two vertical lines (each is a straight line with arrows on both ends), intersecting at a point. Wait, no, actually, there are two horizontal lines (parallel) and one vertical line? No, the diagram has two horizontal lines (each with two arrows) and two vertical lines (each with two arrows), intersecting at two points. Wait, the upper intersection has a \(78^\circ\) angle, and the lower intersection has angle 1. Since the horizontal lines are parallel and the vertical lines are parallel, the angle of \(78^\circ\) and angle 1 are equal (corresponding angles). So angle 1 is \(78\)? Wait, no, wait, maybe the angle of \(78^\circ\) and angle 1 are vertical angles? No, vertical angles are opposite each other. Wait, maybe the angle of \(78^\circ\) and angle 1 are equal because the lines are parallel. Wait, I think I'm overcomplicating. The key is that the two horizontal lines are parallel, and the transversal (vertical line) creates corresponding angles, so angle 1 is equal to \(78^\circ\). Wait, but maybe it's a case of alternate interior angles. Anyway, the measure of angle 1 is \(78\)? Wait, no, wait, maybe the angle of \(78^\circ\) and angle 1 are supplementary? No, that would be if they are adjacent and form a linear pair, but in this case, the lines are parallel, so corresponding angles are equal. So angle 1 is \(78\). Wait, but let me check again. The diagram: two horizontal lines (parallel) and two vertical lines (parallel)? No, the vertical lines are the same line? Wait, no, the diagram has two horizontal lines (each with two arrows) and two vertical lines (each with two arrows), intersecting at two points. The upper intersection has a \(78^\circ\) angle between the upper vertical and upper horizontal. The lower intersection has angle 1 between the lower vertical and lower horizontal. Since the horizontal lines are parallel and the vertical lines are parallel, the angle at the upper intersection and the angle at the lower intersection are equal (corresponding angles). So angle 1 is \(78\). Wait, but maybe I'm wrong. Wait, no, the correct answer is \(78\)? Wait, no, wait, maybe the angle of \(78^\circ\) and angle 1 are vertical angles? No, vertical angles are opposite each other at the same intersection. Wait, maybe the two horizontal lines are the same line? No, the diagram shows two horizontal lines (one above, one below) and two vertical lines (one on the left, one on the right). Wait, no, the diagram has two horizontal lines (each is a straight line with arrows on both ends) and two vertical lines (each is a straight line with arrows on both ends), intersecting at two points. The upper intersection: the angle between the upper vertical (going up) and upper horizontal (going right) is \(78^\circ\). The lower intersection: the angle between the lower vertical (going down) and lower horizontal (going right) is angle 1. Since the horizontal lines are parallel and the vertical lines are parallel, the angle at the upper intersection and the angle at the lower intersection are equal (corresponding angles). So angle 1 is \(78\). Wait, but maybe the angle of \(78^\circ\) and angle 1 are supplementary? No, that would be if they are on a straight line, but they are on parallel lines. So I think angle 1 is \(78\).

Step2: Confirm the angle measure

Since the lines are parallel and the transversal creates corresponding angles, angle 1 is equal to \(78^\circ\). So the measure of angle 1 is \(78\).

Answer:

78