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We are given that \( m\angle ABC = 72^\circ \), and we are tasked with finding \( m\angle 1 \) and \( m\angle 2 \), knowing that \( m\angle 1 = 3m\angle 2 \).

### Step-by-step solution:

1. From the diagram, we can see that \( \angle ABC \) is the sum of \( \angle 1 \) and \( \angle 2 \):
   \[
   m\angle ABC = m\angle 1 + m\angle 2
   \]
   We know that \( m\angle ABC = 72^\circ \), so:
   \[
   72^\circ = m\angle 1 + m\angle 2
   \]

2. We are also given that \( m\angle 1 = 3m\angle 2 \). So, we can substitute this into the first equation:
   \[
   72^\circ = 3m\angle 2 + m\angle 2
   \]
   Simplifying the right-hand side:
   \[
   72^\circ = 4m\angle 2
   \]

3. Solve for \( m\angle 2 \):
   \[
   m\angle 2 = \frac{72^\circ}{4} = 18^\circ
   \]

4. Now that we know \( m\angle 2 = 18^\circ \), substitute this back into the equation \( m\angle 1 = 3m\angle 2 \) to find \( m\angle 1 \):
   \[
   m\angle 1 = 3 \times 18^\circ = 54^\circ
   \]

### Final Answer:
- \( m\angle 1 = 54^\circ \)
- \( m\angle 2 = 18^\circ \)

Would you like further details or clarifications on any steps?

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Here are some related questions to deepen your understanding:

1. What happens if \( m\angle 1 = 2m\angle 2 \) instead of \( 3m\angle 2 \)?
2. Can you apply the same method to find \( m\angle 1 \) and \( m\angle 2 \) if \( m\angle ABC = 90^\circ \)?
3. What are the properties of supplementary angles, and how do they apply here?
4. How would this problem change if the sum of \( \angle 1 \) and \( \angle 2 \) was greater than \( 180^\circ \)?
5. What is the relationship between adjacent angles in similar geometric figures?

**Tip**: Always substitute known values into equations early to simplify your work later on!

m∠ABC = 72°. Find m∠1 and m∠2, using the information m∠1 = 3m∠2.

Learn how to find angles m∠1 and m∠2 given m∠ABC = 72° and m∠1 = 3m∠2. This problem involves angle addition and algebraic substitution, making it perfect for students in Grades 6-8.

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