The diagram shows a pair of parallel lines cut by a transversal, with the angle labeled $\angle 4$. Based on the image:

• The transversal creates a right angle ($90^\circ$) with one of the parallel lines.
• The labeled $\angle 4$ is adjacent to this $90^\circ$ angle and on the same line.

Using Geometry:

Since the two angles are supplementary (on a straight line), their measures add up to $180^\circ$. Thus: $m\angle 4 + 90^\circ = 180^\circ$

Solving for $m\angle 4$: $m\angle 4 = 180^\circ - 90^\circ = 90^\circ$

Final Answer:

$m\angle 4 = 90^\circ$

Would you like a detailed explanation of any specific part of this? Here are five related questions to deepen your understanding:

1. What are supplementary angles, and how are they identified in parallel line setups?
2. How do we know that the given angle is a right angle from the diagram?
3. What role does the transversal play in geometry involving parallel lines?
4. Can the angles formed by a transversal ever be unequal if the lines are parallel?
5. How would the answer change if the lines weren’t parallel?

Tip: In parallel lines with transversals, alternate interior, corresponding, and vertically opposite angles can help identify unknown measures quickly!