To determine the measure of angle $\angle F$, we use the property of vertically opposite angles. Vertically opposite angles are always equal.

From the diagram:

• The angle marked $55^\circ$ and $\angle F$ are vertically opposite angles.

Thus,
$m\angle F = 55^\circ$

Final Answer:

$m\angle F = 55^\circ$

Would you like a detailed explanation or examples of this concept?

Here are 5 related questions to explore further:

1. What are other properties of vertically opposite angles?
2. Can you calculate supplementary angles in this scenario?
3. How are adjacent angles different from vertically opposite angles?
4. What is the sum of all angles formed at a point?
5. How would this apply if the given angle were a different measure?

Tip: Always look for complementary angle relationships in diagrams to confirm your solution!