The question is asking for the measure of angle $\angle UTV$ based on the diagram provided.

Analysis of the Diagram:

• From the diagram, we can see that:
  • $\angle WTU$ is a right angle (90°).
  • There are two smaller angles:
    • $\angle WTV = 12p^\circ$,
    • $\angle VTU = 6p^\circ$.

We need to determine the value of $p$ so we can calculate $\angle UTV$.

Step-by-Step Solution:

1. Sum of angles in a triangle: The sum of the angles in any triangle is 180°. In triangle $WTV$, we have: $\angle WTV + \angle VWT + \angle WVT = 180^\circ$ Since $\angle VWT = 90^\circ$, the equation becomes: $12p^\circ + 90^\circ + \angle WVT = 180^\circ$ Simplifying: $\angle WVT = 180^\circ - 90^\circ - 12p^\circ$ $\angle WVT = 90^\circ - 12p^\circ$

2. Given options: To match one of the provided choices, $p$ must make the angles work with the options available.

Let me know if you want more details or explanation on specific steps!

Related questions:

1. How do you determine the value of $p$ from an equation?
2. What are the properties of right triangles that are useful in this problem?
3. How do you calculate the sum of angles in any triangle?
4. Can we generalize this approach for other angle calculations?
5. How would this change if the right angle were different from 90°?

Tip: Always remember the basic properties of triangles—especially right triangles, where one angle is always 90°.