To solve this problem, let's analyze the information provided in the question:

1. We have two lines $AB$ and $CD$ that intersect at point $O$, creating four non-linear angles.
2. We know that $\angle AOC = 70^\circ$.
3. Line $OM$ is drawn as the bisector of $\angle BOD$.
4. We need to find the measure of $\angle COM$.

Step-by-Step Solution:

Since $AB$ and $CD$ intersect at $O$, they form four angles around point $O$. Given $\angle AOC = 70^\circ$, the angle opposite to $\angle AOC$, which is $\angle BOD$, is also $70^\circ$ due to the property of vertically opposite angles.

Now, if $OM$ is the bisector of $\angle BOD$, it means that: $\angle BOM = \angle MOD = \frac{\angle BOD}{2} = \frac{70^\circ}{2} = 35^\circ$

Therefore, $\angle COM$ can be calculated as the sum of $\angle AOC$ and $\angle BOM$: $\angle COM = \angle AOC + \angle BOM = 70^\circ + 35^\circ = 105^\circ$

Conclusion

The measure of $\angle COM$ is $105^\circ$. However, this value does not match any of the provided options, which suggests there may be an error in either the question options or an interpretation nuance. Based on the correct calculation, the answer should be $105^\circ$, but please verify the answer choices and any context or additional information if available.

Let me know if you would like a further breakdown or if you have any other questions!

Further Exploration Questions

1. What would the measure of $\angle BOD$ be if $\angle AOC$ were different?
2. How do vertically opposite angles work in intersecting lines?
3. What happens if $OM$ is not a bisector but simply divides $\angle BOD$ into two unequal angles?
4. How do we handle angle measures if the intersecting lines are perpendicular?
5. Can you apply similar steps to solve angles formed by other line intersections?

Tip:

When dealing with intersecting lines, always remember that vertically opposite angles are equal.