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In the provided problem, we are given the following:

- \( m \angle WXZ = 80^\circ \).
- The measure of \( m \angle 2 \) is four times the measure of \( m \angle 1 \).
- We need to find \( m \angle 1 \).

### Solution:

Let:
- \( x \) be the measure of \( m \angle 1 \),
- Then, \( m \angle 2 = 4x \).

The sum of angles \( \angle 1 \) and \( \angle 2 \) should equal \( m \angle WXZ \), since they are adjacent angles that form \( \angle WXZ \). Therefore, we have the equation:

\[
x + 4x = 80^\circ
\]

Simplifying:

\[
5x = 80^\circ
\]

\[
x = \frac{80^\circ}{5} = 16^\circ
\]

Thus, \( m \angle 1 = 16^\circ \).

Would you like further details or explanations on any of the steps?

Here are 5 related questions you could explore:
1. How do adjacent angles in a triangle relate to each other?
2. What is the general method to solve for angles when one is a multiple of another?
3. Can this type of angle relationship appear in polygons other than triangles?
4. How would this problem change if one angle was three times the other instead of four?
5. What is the significance of supplementary angles in geometry problems like this?

**Tip:** In geometry, always check whether angles are complementary (sum to 90°) or supplementary (sum to 180°) to simplify your calculations.

En la siguiente figura, m∠WXZ = 80°, y la medida de m∠2 es cuatro veces mayor que la de m∠1. Hallar m∠1.

Learn how to solve for m∠1 given that m∠WXZ = 80° and m∠2 is four times greater than m∠1. This geometry problem demonstrates how to use proportionality and adjacent angle relationships. Suitable for students in Grades 7-8.

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