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The image you uploaded contains a geometric proof table, where the "Statement" and "Reason" columns are used to justify each step of the proof. Here's a breakdown of the proof so far:

### Statements:
1. \( \angle SWT \cong \angle TWU \)
2. \( m \angle SWT + m \angle TWU = 180^\circ \)
3. \( m \angle SWT + m \angle SWT = 180^\circ \)
4. \( m \angle SWT = 90^\circ \)

### Reasons:
1. Given
2. Angles forming a linear pair sum to \(180^\circ\)
3. Substitution (since \( \angle SWT \cong \angle TWU \), their measures are equal)
4. Properties of addition, subtraction, multiplication, and division (solving \( 2m \angle SWT = 180^\circ \))

It looks like the next step (Statement 5) should likely summarize the conclusion or provide a specific result based on this information, such as proving that \( \angle SWT \) is a right angle.

Would you like to complete the proof with that conclusion, or do you have any specific direction in mind?

### Related Questions:
1. How do you determine that two angles form a linear pair?
2. Why does substitution work when \( \angle SWT \cong \angle TWU \)?
3. How can the properties of equality help in solving geometric proofs?
4. What other theorems use linear pairs of angles in geometry?
5. How can we apply this proof structure to a different set of congruent angles?

#### Tip:
When using properties like linear pairs and congruent angles, always check if their measures can be substituted into equations to simplify the proof.

Prove that angle SWT is a right angle using the given angle congruence and linear pair properties.

This solution demonstrates how to prove that angle SWT is a right angle using the properties of linear pairs and angle congruence. Step-by-step reasoning with substitution and properties of equality are used. Ideal for geometry students in Grades 9-11.

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