Question

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

Explanation:

Step1: Identify angle relationships

The two horizontal lines are parallel, and the vertical line is a transversal. The 78° angle and angle 1 are corresponding angles (or alternate interior angles), so angle 1 = 78°.

Step2: Find angle 2

Angle 1 and angle 2 are supplementary (they form a linear pair), so angle 2 = 180 - 78 = 102? Wait, no, wait. Wait, maybe the two horizontal lines are parallel, and the angle with 78° and angle 2: Wait, maybe I misread. Wait, the two slanted lines: Wait, no, the diagram: the two horizontal (or slanted? Wait, the arrows: the two lines with two arrows are parallel, and the vertical line is a transversal. Wait, the 78° angle and angle 2: Wait, maybe angle 1 is equal to 78° (corresponding angles), and angle 2 is supplementary to angle 1? No, wait, maybe the 78° angle and angle 2 are same - side? Wait, no, let's re - examine.

Wait, actually, the two lines with the double arrows are parallel, and the vertical line is a transversal. The angle of 78° and angle 2: Wait, maybe the 78° angle and angle 2 are supplementary? No, wait, no. Wait, the correct approach: If the two parallel lines are cut by a transversal, and the 78° angle and angle 2: Wait, maybe the 78° angle and angle 2 are same - side interior angles? No, wait, no. Wait, let's think again.

Wait, the angle labeled 78° and angle 1 are alternate interior angles (since the two parallel lines are cut by the transversal), so angle 1 = 78°. Then angle 1 and angle 2 are supplementary (they form a linear pair, so they add up to 180°). So angle 2 = 180 - 78 = 102? Wait, but that seems wrong. Wait, no, maybe the 78° angle and angle 2 are corresponding angles? No, that can't be. Wait, maybe I got the diagram wrong. Wait, the two lines with the single arrow and double arrow: maybe they are parallel, and the vertical line is a transversal. The 78° angle and angle 2: Wait, maybe the 78° angle and angle 2 are equal? No, that doesn't make sense. Wait, no, perhaps the 78° angle and angle 2 are supplementary. Wait, let's check the linear pair. If angle 1 is 78°, then angle 2, being adjacent to angle 1 (forming a linear pair), so angle 2 = 180 - 78 = 102? Wait, but maybe the 78° angle and angle 2 are equal. Wait, no, I think I made a mistake. Wait, the two parallel lines: the angle of 78° and angle 2: maybe they are same - side exterior angles? No, this is confusing. Wait, let's start over.

The diagram shows two parallel lines (the ones with the arrows) cut by a transversal (the vertical line). The angle of 78° and angle 2: Wait, maybe the 78° angle and angle 2 are supplementary. Wait, no, the correct rule: when two parallel lines are cut by a transversal, consecutive interior angles are supplementary. But maybe the 78° angle and angle 2 are consecutive interior angles? Wait, no, the 78° angle is above the top parallel line, and angle 2 is below the bottom parallel line. Wait, maybe the 78° angle and angle 2 are equal. Wait, no, I think I messed up. Wait, the key is that angle 1 is equal to 78° (corresponding angles), and angle 2 is equal to 180 - 78 = 102? Wait, no, that can't be. Wait, maybe the 78° angle and angle 2 are vertical angles? No, vertical angles are equal. Wait, I think I made a mistake in the angle relationship. Let's look at the diagram again (mentally). The two parallel lines (let's call them line a and line b, line a is top, line b is bottom) and the transversal (line c, vertical). The angle between line c and the top parallel line (line a) is 78°, on the right side. Then angle 1 is between line c and the bottom parallel line (line b) on the right side, so angle 1 is equal to 78° (alternate interior angles). Then angle 2 is on the left side of line c, adjacent to angle 1, so angle 1 + angle 2 = 180° (linear pair). So angle 2 = 180 - 78 = 102. Wait, but that seems correct.

Answer:

102