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To solve for \( m\angle 5 \) given that \( m\angle 1 = 126^\circ \), let's analyze the diagram using the properties of angles and parallel lines.

### Step 1: Identify the relationship between angles
- Angle \( \angle 1 \) is given as \( 126^\circ \).
- Angles \( \angle 1 \) and \( \angle 2 \) are on a straight line (linear pair), so:
  \[
  m\angle 2 = 180^\circ - m\angle 1 = 180^\circ - 126^\circ = 54^\circ
  \]

### Step 2: Identify corresponding angles
- The triangles formed by the parallel lines and transversals create corresponding angles:
  \[
  m\angle 5 = m\angle 2 = 54^\circ
  \]

Therefore, \( m\angle 5 = 54^\circ \).

Would you like more details on the steps, or do you have any questions?

Here are some related questions:

1. What is the sum of angles in a triangle?
2. How are corresponding angles identified in parallel lines?
3. Can you explain what a linear pair of angles is?
4. What other angles can be calculated in this diagram?
5. What are alternate interior angles?

**Tip:** Remember that corresponding angles are equal when two parallel lines are cut by a transversal.

Learn how to find angle 5 when angle 1 is given as 126 degrees using geometry principles. This problem involves analyzing angles formed by parallel lines and transversals, specifically focusing on corresponding angles. Suitable for Grades 7-9.

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