In the diagram the marked lines are parallel, and angle 2 = 530 and angle 3 = 710.Find the measure of angle 4.

1. Break Down the Problem

To find the measure of angle 4, we need to analyze the relationships between the given angles (angle 2 and angle 3) and the unknown angle (angle 4) based on the properties of parallel lines and transversals.

2. Relevant Concepts

• When two parallel lines are intersected by a transversal, several angle relationships are formed, including alternate interior angles, corresponding angles, and supplementary angles.
• Given $\angle 2 = 53^\circ$ and $\angle 3 = 71^\circ$, we can determine relationships involving angle 4.

3. Analysis and Detail

Assuming that angle 2 and angle 3 are positioned such that angle 4 is adjacent to angle 3 on the same side of the transversal:

1. Identify Relationships:
   • Angles on a straight line sum to $180^\circ$. Therefore, we can use the relationship between angle 3 and angle 4: $\angle 3 + \angle 4 = 180^\circ$
2. Substitute Known Values: $71^\circ + \angle 4 = 180^\circ$
3. Solve for angle 4: $\angle 4 = 180^\circ - 71^\circ$ $\angle 4 = 109^\circ$

4. Verify and Summarize

• We calculated that $\angle 4 = 109^\circ$. We confirmed the relationships are consistent with the properties of parallel lines.

Final Answer

The measure of angle 4 is $109^\circ$.