In the provided diagram, there are two parallel lines cut by a transversal. The 46° angle and the unknown angle (denoted by the question mark) form an important angle pair.

Identifying the angle pair:

The unknown angle and the 46° angle are supplementary angles because they are on the same side of the transversal and form a linear pair. Linear pairs of angles add up to 180°.

Finding the missing measure:

To find the unknown angle: $x + 46^\circ = 180^\circ$ $x = 180^\circ - 46^\circ = 134^\circ$ Thus, the missing angle is $134^\circ$.

Would you like further details or have any questions?

Related questions:

1. What is the name of the angle pair when angles are on opposite sides of the transversal and inside the parallel lines?
2. How can you identify corresponding angles in this diagram?
3. What theorem supports the idea that the two angles here are supplementary?
4. If another angle in the diagram is given as 46°, how can you find all other angles?
5. What would happen if the parallel lines were not parallel—how would this affect the angle relationship?

Tip: Remember, angles on a straight line always sum to 180°, which helps in identifying many angle pairs like supplementary angles.