To solve for $m \angle AOC$, we can use the fact that the sum of adjacent angles around a point $O$ is $180^\circ$. Specifically:

• $m \angle AOB = 47^\circ$
• $m \angle BOC = 59^\circ$

Since we are looking for $m \angle AOC$, we know:

$m \angle AOC = m \angle AOB + m \angle BOC$

Substitute the given values:

$m \angle AOC = 47^\circ + 59^\circ = 106^\circ$

Thus, the measure of $\angle AOC$ is 106 (no degree symbol as requested).

Would you like more details on this solution or have any questions?

Here are 5 related questions to expand on the topic:

1. How would you find the measure of $\angle COD$?
2. What is the sum of the angles around point $O$?
3. How can adjacent angles be used to solve problems in geometry?
4. What is the difference between adjacent and complementary angles?
5. How would you solve for angles in a similar figure where the angles form a straight line?

Tip: In geometry, always remember that the sum of angles around a point equals 360°, which can help solve many problems involving angles around a central point!