The problem asks to find the measure of the angle marked as $?^\circ$ when $x = 32^\circ$. From the provided diagram, the angle $?^\circ$ appears to be complementary to the angle $x$. Complementary angles sum to $90^\circ$.

Calculation:

$?^\circ = 90^\circ - x$

Substitute $x = 32^\circ$:

$?^\circ = 90^\circ - 32^\circ = 58^\circ$

Final Answer:

The measure of the angle $?^\circ$ is $58^\circ$.

Do you want details or have any questions?
Here are 5 related questions for further exploration:

1. What are complementary angles and how are they used in geometry?
2. If $x$ was $40^\circ$, what would $?^\circ$ be?
3. How are complementary and supplementary angles different?
4. Can you derive $x$ if $?^\circ = 45^\circ$?
5. What are some real-world applications of complementary angles?

Tip: Always check the relationship between angles in diagrams (like complementary, supplementary, or vertical angles) to simplify your calculations.