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The problem provides the value of \( m \angle 4 = 136^\circ \) and asks us to find the measures of \( m \angle 1 \), \( m \angle 2 \), and \( m \angle 3 \). The diagram shows intersecting lines, forming vertical and adjacent angles.

Here are the key steps to solve this:

1. **Vertical Angles**: Vertical angles are equal. Since \( \angle 4 \) is vertical to \( \angle 2 \), we know:
   \[
   m \angle 2 = m \angle 4 = 136^\circ
   \]

2. **Linear Pair**: Adjacent angles that form a straight line sum to \( 180^\circ \). \( \angle 1 \) and \( \angle 4 \) form a linear pair, so:
   \[
   m \angle 1 + m \angle 4 = 180^\circ
   \]
   Substituting the given value of \( m \angle 4 = 136^\circ \):
   \[
   m \angle 1 + 136^\circ = 180^\circ
   \]
   Solving for \( m \angle 1 \):
   \[
   m \angle 1 = 180^\circ - 136^\circ = 44^\circ
   \]

3. **Vertical Angle for \( \angle 3 \)**: Similarly, \( \angle 1 \) and \( \angle 3 \) are vertical angles, so:
   \[
   m \angle 3 = m \angle 1 = 44^\circ
   \]

Thus, the measures are:
- \( m \angle 1 = 44^\circ \)
- \( m \angle 2 = 136^\circ \)
- \( m \angle 3 = 44^\circ \)

Would you like more details or have any questions?

### Related questions:
1. How are vertical angles defined and why are they equal?
2. What is the linear pair relationship in geometry?
3. How can you find the measure of an angle given its adjacent angle?
4. How do intersecting lines affect the measures of angles?
5. What other angle relationships can be formed with intersecting lines?

**Tip**: Always remember that vertical angles are congruent, and adjacent angles on a straight line sum to \(180^\circ\).

In the figure below, m∠4 = 136°. Find m∠1, m∠2, and m∠3.

Learn how to find the measures of angles formed by intersecting lines using the vertical angles theorem and the linear pair relationship. In this problem, given m∠4 = 136°, you'll calculate m∠1, m∠2, and m∠3.

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