https://file.aiquickdraw.com/mathbot/file/1727299596810bed35o4b.jpg

The problem asks to find the measure of angle \( \angle 1 \) given that \( m \angle 2 = 36^\circ \) and \( m \angle TSV = 135^\circ \). The diagram shows that angles \( \angle 1 \), \( \angle 2 \), and \( \angle TSV \) are all part of a geometric configuration.

### Observations:
- \( \angle 1 \) and \( \angle 2 \) form a linear pair, which means they are supplementary because they lie on a straight line.
- Therefore, the sum of \( \angle 1 \) and \( \angle 2 \) must be \( 180^\circ \).

### Steps:
1. Since \( \angle 1 \) and \( \angle 2 \) are supplementary, we use the equation:
   \[
   m \angle 1 + m \angle 2 = 180^\circ
   \]
2. Substituting the given value of \( m \angle 2 = 36^\circ \) into the equation:
   \[
   m \angle 1 + 36^\circ = 180^\circ
   \]
3. Solving for \( m \angle 1 \):
   \[
   m \angle 1 = 180^\circ - 36^\circ = 144^\circ
   \]

Thus, the measure of \( \angle 1 \) is \( 144^\circ \).

Do you have any questions or want further details?

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Here are 5 related questions for further exploration:
1. What is the relationship between angles in a linear pair?
2. How can you verify if two angles are supplementary or complementary?
3. What are vertical angles, and how do they relate to the angles shown in the diagram?
4. How can angle relationships be used to solve for unknown angles in a triangle?
5. What are some common types of angle pairs found in geometric diagrams?

**Tip:** Always remember that angles on a straight line sum up to \( 180^\circ \).

In the figure below, m∠2 = 36° and m∠TSV = 135°. Find m∠1.

Learn how to solve for the measure of angle 1 when m∠2 = 36° and m∠TSV = 135°. This geometry problem explains the linear pair and supplementary angle concepts, suitable for students in Grades 8-10.

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