https://file.aiquickdraw.com/mathbot/file/1729857060039gposlz0v.jpg

Let's solve the problem step by step:

We are given:
- \( m \angle WXZ = 113^\circ \) 
- \( m \angle 2 \) is 11° more than \( m \angle 1 \)

### Step 1: Set up equations
Let \( m \angle 1 = x \). Then,
\[
m \angle 2 = x + 11^\circ
\]
Since angles \( \angle 1 \) and \( \angle 2 \) are adjacent and together form the angle \( \angle WXZ \), we know:
\[
m \angle WXZ = m \angle 1 + m \angle 2
\]
Substituting the known values:
\[
113^\circ = x + (x + 11^\circ)
\]
Simplifying:
\[
113^\circ = 2x + 11^\circ
\]
### Step 2: Solve for \( x \)
\[
113^\circ - 11^\circ = 2x
\]
\[
102^\circ = 2x
\]
\[
x = \frac{102^\circ}{2} = 51^\circ
\]

Thus, \( m \angle 1 = 51^\circ \).

### Conclusion:
The measure of \( \angle 1 \) is \( 51^\circ \).

Let me know if you would like further details or clarifications!

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### Here are some related questions:
1. What would be the value of \( m \angle 2 \) in the figure?
2. How would the solution change if \( m \angle WXZ \) was a different value?
3. What is the sum of all angles around point \( X \) in this case?
4. Can you determine the value of \( m \angle WXY \)?
5. How do adjacent angles relate in a straight line configuration?

### Tip:
Always remember that the sum of angles around a point equals \( 360^\circ \). This can help when solving problems involving adjacent or complementary angles.

In the figure below, m∠WXZ = 113°, and m∠2 is 11° more than m∠1. Find m∠1.

Learn how to find m∠1 in a geometric problem where m∠WXZ = 113°, and m∠2 is 11° more than m∠1. This solution covers key geometry concepts, angle properties, and adjacent angles. Suitable for students in Grades 6-8.

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