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This problem involves a pair of supplementary angles.

From the diagram, it is clear that:

- \( \angle 1 \) and \( \angle 2 \) are adjacent angles formed by a straight line, which means they are supplementary angles.
- The sum of supplementary angles is always \( 180^\circ \).

Given that \( m \angle 2 = 64^\circ \), we can find \( m \angle 1 \) by subtracting the measure of \( \angle 2 \) from \( 180^\circ \):

\[
m \angle 1 = 180^\circ - m \angle 2
\]
\[
m \angle 1 = 180^\circ - 64^\circ = 116^\circ
\]

Thus, \( m \angle 1 = 116^\circ \).

Would you like a further breakdown of how supplementary angles work or any additional details?

Here are 5 related questions you might find interesting:
1. What are complementary angles, and how are they different from supplementary angles?
2. How do vertical angles relate to adjacent angles?
3. Can two obtuse angles be supplementary? Why or why not?
4. How would the calculation change if the angles were on a transversal line with parallel lines?
5. How can we apply the concept of supplementary angles in real-world geometry problems?

**Tip**: In any problem involving angles on a straight line, always check for supplementary relationships since the sum will always be \( 180^\circ \).

Solve for the measure of angle 1 when given that angle 2 is 64 degrees in a supplementary angles pair. Understand the concept of supplementary angles where the sum of the angles is 180 degrees. Suitable for students in Grades 6-8.

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