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The problem states:

- Point \( B \) is in the interior of \( \angle AOC \).
- \( m\angle AOC = 108^\circ \).
- \( m\angle AOC = 3 \times m\angle AOB \).

We are asked to find \( m\angle AOB \).

### Step-by-Step Solution:

1. Let \( x = m\angle AOB \). This is the unknown angle we need to find.
   
2. According to the problem, \( m\angle AOC = 3 \times m\angle AOB \). So we can write the equation:
   \[
   108^\circ = 3 \times x
   \]

3. Solve for \( x \):
   \[
   x = \frac{108^\circ}{3} = 36^\circ
   \]

Thus, \( m\angle AOB = 36^\circ \).

Would you like a more detailed explanation of any part? 

Here are 5 related questions to further explore this concept:
1. What is the relationship between angles formed by a point on the interior of an angle?
2. How can you use algebra to solve for unknown angle measures in geometric problems?
3. If \( m\angle AOC = 4 \times m\angle AOB \), how would the problem change?
4. Can you explain what happens to \( m\angle AOB \) if \( m\angle AOC \) is doubled?
5. How would you calculate the angle if point B was not in the interior of the angle?

### Tip:
Always check if there are additional constraints or relationships between angles in geometric figures, as these often help solve the problem faster.

Point B is in the interior of ∠AOC; m∠AOC = 108°, and m∠AOC = 3 × m∠AOB. Find m∠AOB.

Learn how to solve for the measure of angle AOB when it is given that m∠AOC is three times m∠AOB and m∠AOC = 108°. This geometry problem explores angle relationships and proportionality, ideal for students in Grades 7-9.

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