To solve this problem, we are asked to find the measure of angle $\angle AOB$ given two angles:

• $\angle BOC = 27^\circ$
• $\angle AOC = 47^\circ$

We can apply the following reasoning:

1. $\angle AOC$ is the larger angle that encompasses both $\angle AOB$ and $\angle BOC$. Therefore, we can break down the larger angle into two parts: $\angle AOC = \angle AOB + \angle BOC$

2. Substitute the known values into the equation: $47^\circ = \angle AOB + 27^\circ$

3. Solve for $\angle AOB$: $\angle AOB = 47^\circ - 27^\circ = 20^\circ$

So, the measure of $\angle AOB$ is $20^\circ$.

The correct answer is 20.

Would you like more details or have any questions?

Here are 5 questions to explore further:

1. How would the solution change if the measure of $\angle AOC$ was different?
2. What types of geometric problems can be solved using angle addition?
3. How can you verify angle measures when the diagram is not to scale?
4. How do different angle relationships, such as adjacent and supplementary angles, work in problems like this?
5. What strategies can help in solving problems involving multiple angles and intersections?

Tip: Always remember that diagrams may not be to scale in geometry problems. Rely on given information rather than visual estimates.