Let's solve each problem step-by-step.

Problem 1

1. Given Angle: $80^\circ$
2. Angle Relationship: Since the angles are on opposite sides of the transversal and are formed by parallel lines, they are corresponding angles.
3. Missing Angle Measure: By the Corresponding Angles Postulate, corresponding angles are equal. Therefore, $x = 80^\circ$.

Problem 2

1. Given Angle: $118^\circ$
2. Angle Relationship: The angles are on opposite sides of the transversal and outside the parallel lines, making them alternate exterior angles.
3. Missing Angle Measure: Alternate exterior angles are congruent, so $x = 118^\circ$.

Problem 3

1. Given Angle: $158^\circ$
2. Angle Relationship: These angles are also on opposite sides of the transversal and outside the parallel lines, so they are alternate exterior angles.
3. Missing Angle Measure: Since alternate exterior angles are equal, $x = 158^\circ$.

Would you like further details on any of these solutions?

Additional Related Questions

1. How can you identify corresponding angles in other diagrams?
2. What are the key properties of alternate interior angles?
3. How do supplementary angles differ from complementary angles in these configurations?
4. What role does the transversal line play in determining angle relationships?
5. Can you provide an example of when alternate interior angles are equal?

Tip

Remember that parallel lines cut by a transversal create several angle pairs, and recognizing these relationships helps solve for unknown angles quickly.