https://file.aiquickdraw.com/mathbot/file/1730145101487pqztv6l3.jpg

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

1. We are given:
   - \( m \angle 1 = 83^\circ \)
   - \( m \angle TSW = 141^\circ \)

2. In the figure, \( \angle TSW \) is the entire angle formed by the two rays \( TS \) and \( SW \). This angle is composed of:
   - \( \angle 1 \) (which is \( 83^\circ \))
   - \( \angle 2 \) (which we need to find)

Since \( m \angle TSW = m \angle 1 + m \angle 2 \), we can set up the equation:

\[
m \angle TSW = m \angle 1 + m \angle 2
\]

Substitute the known values:

\[
141^\circ = 83^\circ + m \angle 2
\]

To find \( m \angle 2 \), subtract \( 83^\circ \) from \( 141^\circ \):

\[
m \angle 2 = 141^\circ - 83^\circ
\]

\[
m \angle 2 = 58^\circ
\]

### Answer:
\[
m \angle 2 = 58^\circ
\]

Would you like more details, or do you have any questions about this solution?

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Here are some related questions you might find interesting:

1. What is the sum of angles in a straight line, and how does it apply to problems like these?
2. How can we find the measure of unknown angles in polygons?
3. What methods can be used to solve for unknown angles in intersecting lines?
4. How can complementary and supplementary angles help in solving geometry problems?
5. How do angles around a point relate to each other?

#### Tip:
Always double-check which angles are adjacent or form a part of a larger angle to set up the correct equations.

In the figure below, m∠1 = 83° and m∠TSW = 141°. Find m∠2.

This problem demonstrates how to find the measure of an unknown angle (m∠2) by using the angle addition postulate. Given that m∠1 = 83° and m∠TSW = 141°, students can follow a step-by-step solution to determine m∠2. This exercise is ideal for students in Grades 6-8 learning about basic geometry and angle relationships.

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