Geometry problems involving parallel lines and transversals, including angle calculations. (Questions 3, 4, and 5 are shown.)

The diagram shows two parallel lines intersected by a zigzag transversal. The angles are $x^\circ$, $78^\circ$, and $80^\circ$.

This rule states that for a transversal zigzagging between two parallel lines, the sum of the angles pointing in one direction equals the sum of the angles pointing in the opposite direction.
Visually, $x^\circ$ and $80^\circ$ appear to be "left turns" or angles opening to the left, while $78^\circ$ appears to be a "right turn" or an angle opening to the right.
If we apply the rule directly as (sum of left turns) = (sum of right turns):

However, angles in geometry problems are typically positive. In such zigzag problems, it is common for the largest angle to be the sum of the other two, or for the "middle" angle to be the sum of the "outer" angles.

Let's consider the possibility that the angle $80^\circ$ is the sum of the other two angles, $x^\circ$ and $78^\circ$. This often happens when the largest angle "encompasses" the other turns.

This gives a positive and plausible value for $x$.