Question

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

Explanation:

Step1: Identify angle relationship

The two lines are parallel (indicated by the arrow marks), and the transversal creates corresponding angles or supplementary angles? Wait, actually, angle 2 and the 87° angle are same - side interior angles? No, wait, looking at the diagram, the two vertical lines are parallel, and the horizontal line is a transversal. Wait, no, the two vertical lines (with arrows) are parallel, and the horizontal line intersects them. Wait, angle 2 and the 87° angle: actually, they are same - side? No, wait, the angle adjacent to 87° and angle 2: Wait, the sum of angle 2 and 87° should be 180°? No, wait, no. Wait, the two vertical lines are parallel, and the horizontal line is a transversal. Wait, angle 2 and the angle of 87°: are they corresponding angles? No, wait, maybe alternate interior angles? Wait, no, let's think again. Wait, the two vertical lines are parallel, so the angle equal to 87° and angle 2: Wait, no, the angle marked 87° and angle 2: if the lines are parallel, then angle 2 and 87° are supplementary? Wait, no, 180 - 87 = 93? Wait, no, wait, maybe I made a mistake. Wait, the diagram: two parallel lines (vertical) cut by a transversal (horizontal). The angle between the transversal and one parallel line is 87°, and angle 2 is on the other parallel line. Wait, actually, angle 2 and the 87° angle are same - side interior angles? No, same - side interior angles are supplementary. Wait, 180 - 87 = 93? Wait, no, wait, maybe the angle is equal? No, that can't be. Wait, no, the two vertical lines are parallel, so the corresponding angles should be equal. Wait, maybe the angle adjacent to 87° is 93°, and angle 2 is equal to that? Wait, let's see: the straight line (transversal) forms a linear pair with 87°, so 180 - 87 = 93. Then, since the two vertical lines are parallel, angle 2 is equal to that 93° angle (corresponding angles or alternate interior angles). So angle 2 = 93.

Step2: Calculate angle 2

Since the sum of a linear pair is 180°, the angle supplementary to 87° is $180 - 87 = 93$. And since the two vertical lines are parallel, angle 2 is equal to this supplementary angle (by corresponding angles or alternate interior angles theorem). So angle 2 = 93.

Answer:

93