Based on the diagram and the problem, here is the step-by-step reasoning for finding the measure of angle 5:

1. Given information:

   • Angle 1 is $84^\circ$.
   • Angles are labeled, and the lines appear to form transversals and intersecting pairs.

2. Step-by-step reasoning:

   • Angle 1 and angle 3 are vertical angles, so angle 3 is also $84^\circ$.
   • Angle 3 and angle 5 are corresponding angles (formed by a transversal cutting parallel lines), so angle 5 must also be $96^\circ$.
   • This satisfies the property of corresponding angles, where the measures are equal.

3. Correct option:

   • The correct answer is (c): $96^\circ$, corresponding to angle 4, which is supplementary to angle 5.

Would you like further clarification or additional help on this?

Here are 5 related questions for deeper understanding:

1. What are vertical angles and how are their measures related?
2. How do corresponding angles behave when a transversal intersects parallel lines?
3. Why are supplementary angles important in solving problems involving angles and parallel lines?
4. Can you explain the difference between alternate interior and alternate exterior angles?
5. How would the problem change if the lines in the diagram were not parallel?

Tip: Always double-check the relationships (e.g., corresponding, vertical, alternate) between angles when solving geometry problems.