In the diagram the marked lines are parallel, and angle 1 = 580 and angle 3 = angle 5.Find the measure of angle 3.

1. Break Down the Problem

We need to find the measure of angle 3, using the information that angle 1 = 58° and that angles 3 and 5 are equal. Since the marked lines are parallel, we can use the properties of angles formed by parallel lines and a transversal.

2. Relevant Concepts

When two parallel lines are crossed by a transversal, the following angle relationships are useful:

• Corresponding angles are equal.
• Alternate interior angles are equal.
• Consecutive interior angles are supplementary (sum to 180°).

3. Analysis and Detail

1. Given angle 1 = 58°, identify its position relative to angles 3 and 5.
2. If angle 1 corresponds to angle 5 (due to the parallel lines), then: $\text{Angle 5} = \text{Angle 1} = 58°$
3. Since angle 3 is equal to angle 5: $\text{Angle 3} = \text{Angle 5} = 58°$

4. Verify and Summarize

Through the properties of parallel lines and transversals, we confirmed that angles 5 and 1 are corresponding angles, which leads to angle 3 being equal to angle 5.

Final Answer

The measure of angle 3 is $58°$.