Since angles $F$ and $H$ are supplementary, their measures add up to $180^\circ$. This relationship gives us the following equation:

$77 + (5x + 18) = 180$

So, the correct answer is:

B. $77 + (5x + 18) = 180$

Would you like further details or have any questions?

Here are some additional questions to expand on this topic:

1. What is the definition of complementary angles, and how does it differ from supplementary angles?
2. How would you solve for $x$ using the equation we identified?
3. What is the measure of angle $H$ once you find the value of $x$?
4. Can two obtuse angles be supplementary? Why or why not?
5. How would the equation change if angles $F$ and $H$ were complementary instead?

Tip: Always remember that supplementary angles add up to $180^\circ$, while complementary angles add up to $90^\circ$.