https://file.aiquickdraw.com/mathbot/file/1730152927222akvee589.jpg

To solve for \( m \angle 2 \), let's analyze the information given in the problem.

### Problem Information:
1. The angle \( m \angle WXZ = 96^\circ \).
2. \( m \angle 1 \) is three times \( m \angle 2 \).
3. We need to find \( m \angle 2 \).

### Step-by-Step Solution:
1. Since \( m \angle 1 \) and \( m \angle 2 \) are adjacent angles that form the entire angle \( \angle WXZ \), we have:
   \[
   m \angle 1 + m \angle 2 = m \angle WXZ
   \]
   So,
   \[
   m \angle 1 + m \angle 2 = 96^\circ
   \]

2. Given that \( m \angle 1 \) is three times \( m \angle 2 \), we can express \( m \angle 1 \) as:
   \[
   m \angle 1 = 3 \times m \angle 2
   \]

3. Substitute \( m \angle 1 = 3 \times m \angle 2 \) into the equation from step 1:
   \[
   3 \times m \angle 2 + m \angle 2 = 96^\circ
   \]

4. Combine like terms:
   \[
   4 \times m \angle 2 = 96^\circ
   \]

5. Solve for \( m \angle 2 \):
   \[
   m \angle 2 = \frac{96^\circ}{4} = 24^\circ
   \]

### Conclusion:
The measure of \( m \angle 2 \) is:
\[
\boxed{24^\circ}
\]

Would you like further details or have any questions?

---

#### Related Questions:
1. What would \( m \angle 1 \) be in this problem?
2. How can we generalize this method for other problems where one angle is a multiple of another?
3. What if \( m \angle WXZ \) were a different value, how would it affect \( m \angle 2 \)?
4. How can we apply similar steps if we know the sum but not the ratio between two angles?
5. What are some properties of adjacent angles in geometry?

#### Tip:
When angles are expressed in terms of each other, try setting up equations based on known relationships, such as sum or multiple, to simplify finding unknown values.

In the figure below, m ∠WXZ = 96°, and m ∠1 is three times m ∠2. Find m ∠2.

Solve for the measure of angle m ∠2 in the geometry problem where m ∠WXZ = 96° and m ∠1 is three times m ∠2. This solution covers angle addition and ratio-based relationships, suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation