Question

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

Explanation:

Step1: Identify angle relationship

The lines are parallel (since they are both perpendicular to the same transversal, or from the diagram's parallel arrows), so angle 1 and the 87° angle are same - side interior angles? Wait, no, actually, looking at the diagram, the two vertical lines are parallel, and the horizontal line is a transversal. Wait, no, the angle given is 87°, and angle 1 and that angle should be supplementary? Wait, no, actually, if we consider the vertical angles and parallel lines, angle 1 and the 87° angle: wait, no, let's think again. The two vertical lines are parallel, and the horizontal line is a transversal. The angle of 87° and angle 1: since the lines are parallel, and the transversal, the consecutive interior angles? Wait, no, actually, the angle adjacent to 87° and angle 1: wait, maybe they are alternate interior angles? No, wait, the sum of angle 1 and 87° should be 180°? Wait, no, that can't be. Wait, no, looking at the diagram, the two vertical lines are parallel, and the horizontal line is a transversal. The angle marked 87° and angle 1: if we consider that the two vertical lines are parallel, then the corresponding angles or alternate interior angles. Wait, no, actually, the angle 1 and the 87° angle: since the lines are parallel, and the transversal, angle 1 and 87° are same - side? No, wait, maybe they are supplementary? Wait, no, 180 - 87 = 93? No, that's not right. Wait, no, the diagram shows two parallel lines (the vertical ones) cut by a transversal (the horizontal one). The angle given is 87°, and angle 1: since the lines are parallel, the alternate interior angles? Wait, no, maybe the angle 1 and 87° are equal? No, that doesn't make sense. Wait, no, let's look at the diagram again. The two vertical lines are parallel, and the horizontal line is a transversal. The angle of 87° and angle 1: if we consider that the angle adjacent to 87° is 93°, but no. Wait, maybe the lines are perpendicular? No, the diagram has two sets of parallel lines (the vertical ones and the horizontal ones? No, the vertical lines are parallel, and the horizontal line is a transversal. Wait, the key is that angle 1 and the 87° angle are supplementary? Wait, no, 180 - 87 = 93? No, that's not. Wait, no, the correct relationship: when two parallel lines are cut by a transversal, consecutive interior angles are supplementary. Wait, the angle 87° and angle 1: are they consecutive interior angles? Let's see, the two vertical lines are parallel, the horizontal line is the transversal. So angle 1 and the 87° angle: if we consider the direction, angle 1 and 87° should be supplementary? Wait, 180 - 87 = 93? No, that's not. Wait, maybe I made a mistake. Wait, the diagram: the two vertical lines are parallel, and the horizontal line is a transversal. The angle marked 87° and angle 1: actually, angle 1 is equal to 87°? No, that can't be. Wait, no, the correct approach: the sum of angle 1 and 87° is 180°? Wait, no, 180 - 87 = 93? Wait, no, maybe the lines are perpendicular, but no. Wait, let's think again. The diagram shows two parallel lines (vertical) and a transversal (horizontal). The angle between the transversal and one vertical line is 87°, so the angle between the transversal and the other vertical line (angle 1) should be equal to 87°? No, that's alternate interior angles. Wait, alternate interior angles are equal. So if the two vertical lines are parallel, and the horizontal line is the transversal, then angle 1 and the 87° angle are alternate interior angles, so they are equal? But that would be 87, but that doesn't make sense. Wait, no, maybe the angle is 180 - 87 = 93. Wait, I think I messed up. Let's recall: when two parallel lines are cut by a transversal, consecutive interior angles are supplementary. So if one angle is 87°, the consecutive interior angle is 180 - 87 = 93°. So angle 1 is 93? Wait, no, let's check the diagram again. The two vertical lines are parallel, the horizontal line is the transversal. The angle marked 87° and angle 1: are they consecutive interior angles? Yes, because they are on the same side of the transversal and inside the two parallel lines. So consecutive interior angles are supplementary, so angle 1 + 87° = 180°. So angle 1 = 180 - 87 = 93.

Step2: Calculate angle 1

We know that consecutive interior angles are supplementary, so the formula is $\text{angle 1} = 180 - 87$.
Calculating $180 - 87 = 93$.

Answer:

93