To solve this, we start by noting that angles $P$ and $Q$ are adjacent and their sum is $180^\circ$. Thus, we can write:

$P + Q = 180^\circ$

Since we know:

• $P = (3x + 15)^\circ$
• $Q = 45^\circ$

we substitute these values into the equation:

$3x + 15 + 45 = 180$

Now, let’s see if this matches any of the answer choices:

Answer: A. $3x + 15 + 45 = 180$

Would you like to go through solving this equation for $x$ or have any questions on this?

Here are some related questions:

1. How would you solve the equation $3x + 15 + 45 = 180$?
2. What would happen if angles $P$ and $Q$ were not adjacent?
3. What are adjacent angles, and how do they differ from complementary angles?
4. What is the definition of supplementary angles?
5. Can adjacent angles also be complementary? If so, when?

Tip: Always check if angles are complementary (sum to 90°) or supplementary (sum to 180°) based on the context of the problem.