Given:
In the given figure, AB is perpendicular to CD.

To find:
We need to find the measure of angle AOC.

Explanation:

1. Understanding the given information:
- We are given a figure with two intersecting lines AB and CD.
- AB is perpendicular to CD, which means that AB forms a 90-degree angle with CD.
- We are also given that angle BAO is 60 degrees and angle OCD is 110 degrees.

2. Understanding the properties of perpendicular lines:
- When two lines are perpendicular, the angles formed on either side of the point of intersection are complementary, which means they add up to 90 degrees.
- In this case, angle BAO and angle AOC are complementary angles because they are formed on either side of the point of intersection.
- Similarly, angle OCD and angle AOC are also complementary angles.

3. Applying the properties of perpendicular lines:
- Since angle BAO is 60 degrees and angle AOC is complementary to it, we can find angle AOC by subtracting 60 degrees from 90 degrees.
- Similarly, since angle OCD is 110 degrees and angle AOC is complementary to it, we can find angle AOC by subtracting 110 degrees from 90 degrees.
- Therefore, the measure of angle AOC is 90 - 60 = 30 degrees or 90 - 110 = -20 degrees.

4. Determining the valid measure of angle AOC:
- Since angles cannot have negative measures, we discard the -20 degrees solution.
- Hence, the valid measure of angle AOC is 30 degrees.

Conclusion:
The measure of angle AOC is 30 degrees.

Where is the figure.....??