In the given figure:

• You are provided with two intersecting lines forming several angles around point $O$.
• The angle $\angle AOB = 110^\circ$, and we are asked to find the value of $x$, which is the measure of $\angle EOD$, knowing that line $OC$ bisects $\angle BOD$.

Let's proceed step by step:

1. $\angle AOB$ and $\angle EOD$ are vertically opposite angles, meaning they are equal. Therefore, $x = 110^\circ$

Thus, $x = 110^\circ$.

Would you like further clarification on vertical angles, or do you have any other questions?

Related Questions:

1. What are vertically opposite angles, and how are they related?
2. How does an angle bisector work in geometry?
3. How can we find the sum of angles at a point?
4. What are the properties of supplementary angles?
5. How do adjacent angles differ from vertically opposite angles?

Tip: In geometry, always look for relationships like vertical angles or angle bisectors to simplify the problem-solving process.