Question

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

Explanation:

Step1: Identify angle relationships

The angle of \(78^\circ\) and angle 1 are complementary? No, wait, looking at the lines, the two horizontal lines are parallel (since they are both horizontal), and the vertical line is a transversal? Wait, no, actually, the angle of \(78^\circ\) and angle 1: Wait, maybe angle 1 is equal to \(78^\circ\) because they are corresponding angles? Wait, no, let's see: the two horizontal lines are parallel, and the vertical line is a transversal? Wait, no, actually, the angle of \(78^\circ\) and angle 1: Wait, maybe angle 1 is equal to \(78^\circ\) (corresponding angles). Then angle 1 and angle 2: are they supplementary? Wait, no, angle 1 and angle 2: if angle 1 is \(78^\circ\), then angle 2 would be \(180 - 78 = 102\)? Wait, no, wait, maybe I got it wrong. Wait, the angle of \(78^\circ\) and angle 1: are they alternate interior angles? Wait, no, let's look at the diagram again. The two horizontal lines are parallel, and the vertical line is a transversal? Wait, no, actually, the angle of \(78^\circ\) and angle 1: maybe angle 1 is \(78^\circ\) (vertical angles? No, vertical angles are equal. Wait, the angle of \(78^\circ\) and angle 1: if the two horizontal lines are parallel, then the angle of \(78^\circ\) and angle 1 are corresponding angles, so angle 1 is \(78^\circ\). Then angle 1 and angle 2: are they supplementary? Wait, no, angle 1 and angle 2: if they are adjacent and form a linear pair, then angle 1 + angle 2 = 180? Wait, no, wait, maybe angle 2 is equal to \(180 - 78 = 102\)? Wait, no, wait, maybe I made a mistake. Wait, the angle of \(78^\circ\) and angle 2: are they same - side interior angles? Wait, no, let's think again. The two horizontal lines are parallel, and the vertical line is a transversal. The angle of \(78^\circ\) and angle 2: if angle 1 is \(78^\circ\) (corresponding to \(78^\circ\)), then angle 2 and angle 1: are they supplementary? Wait, no, angle 1 and angle 2: if they are adjacent and form a linear pair, then angle 1 + angle 2 = 180. Wait, no, maybe angle 2 is equal to \(180 - 78 = 102\)? Wait, no, wait, the correct approach: the angle of \(78^\circ\) and angle 1 are equal (corresponding angles, since the two horizontal lines are parallel and the vertical line is a transversal). Then angle 1 and angle 2 are supplementary (linear pair), so angle 2 = \(180 - 78 = 102\)? Wait, no, wait, maybe angle 2 is equal to \(78^\circ\)? No, that can't be. Wait, maybe the two horizontal lines are not parallel, but the vertical line is intersecting them. Wait, the angle of \(78^\circ\) and angle 2: are they vertical angles? No, vertical angles are opposite. Wait, maybe the angle of \(78^\circ\) and angle 1 are vertical angles? No, the angle of \(78^\circ\) and angle 1: if the two horizontal lines are parallel, then angle 1 is \(78^\circ\) (alternate interior angles). Then angle 1 and angle 2: are they supplementary? Wait, no, angle 1 and angle 2: if they are adjacent and form a linear pair, then angle 1 + angle 2 = 180. So angle 2 = \(180 - 78 = 102\)? Wait, no, maybe I'm overcomplicating. Wait, the angle of \(78^\circ\) and angle 2: are they same - side? Wait, the correct answer is that angle 2 is equal to \(180 - 78 = 102\)? No, wait, maybe angle 2 is equal to \(78^\circ\)? No, that's not right. Wait, let's look at the diagram again. The two horizontal lines are parallel, and the vertical line is a transversal. The angle of \(78^\circ\) and angle 1 are corresponding angles, so angle 1 = \(78^\circ\). Then angle 1 and angle 2 are supplementary (linear pair), so angle 2 = \(180 - 78 = 102\). Wait, but maybe angle 2 is equal to \(78^\circ\)? No, that would be if they are alternate interior angles, but no, angle 1 and angle 2 are adjacent. Wait, I think I made a mistake. Wait, the angle of \(78^\circ\) and angle 2: are they vertical angles? No, vertical angles are opposite. Wait, maybe the two horizontal lines are not parallel, but the vertical line is intersecting them. Wait, the angle of \(78^\circ\) and angle 2: if the two horizontal lines are parallel, then angle 2 is equal to \(180 - 78 = 102\). Wait, but let's check again. The angle of \(78^\circ\) and angle 1: are they equal (corresponding angles), so angle 1 = \(78^\circ\). Then angle 1 and angle 2: linear pair, so angle 2 = \(180 - 78 = 102\). Yes, that makes sense.

Step2: Calculate angle 2

Since angle 1 and the \(78^\circ\) angle are corresponding angles (parallel lines, transversal), angle 1 = \(78^\circ\). Then angle 1 and angle 2 form a linear pair, so angle 2 = \(180 - 78 = 102\).

Answer:

102