tions 17-20, use the diagram of the indicated angle. 17.) $$ m \angle P T R= $$ $$ \qquad $$ 9 $$ \qquad $$ 18.) $$ m \angle U T R= $$ 19.) $$ \quad m \angle S T P= $$ $$ \qquad $$ 20.) $$ \quad m \angle P T U= $$ $$ \qquad $$ $$ 180^{\circ} $$

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UpStudy AI · Accepted Answer

It looks like you're referring to specific geometry problems (questions 17-20) that involve measuring angles based on a given diagram. Unfortunately, without the diagram, it's challenging to provide precise answers. However, I can offer some general guidance on how to approach these types of angle measurement problems:

### General Steps to Solve Angle Measurement Problems:

1. **Identify Relationships:**
   - **Vertical Angles:** Opposite angles formed by two intersecting lines are equal.
   - **Adjacent Angles:** Angles that are next to each other and share a common side.
   - **Complementary Angles:** Two angles whose measures add up to $$90^\circ$$.
   - **Supplementary Angles:** Two angles whose measures add up to $$180^\circ$$.

2. **Use Given Information:**
   - Start with the angle measurements provided in the problem.
   - Apply geometric properties and theorems relevant to the situation.

3. **Set Up Equations:**
   - Based on the relationships, set up equations to solve for the unknown angles.

4. **Solve for the Unknowns:**
   - Use algebraic methods to find the measures of the unknown angles.

### Applying to Your Problems:

While I don't have the specific diagram, here's how you might approach each question based on typical angle relationships:

1. **Question 17: $$ m \angle PTR = 9 $$**
   - It seems like this angle is given as $$9^\circ$$.
   
2. **Question 18: $$ m \angle UTR = $$**
   - To find this, identify if it's vertical, complementary, or supplementary to a known angle.
   
3. **Question 19: $$ m \angle STP = $$**
   - Determine the relationship of this angle with others in the diagram to set up an equation.
   
4. **Question 20: $$ m \angle PTU = 180^\circ $$**
   - This suggests that $$ \angle PTU $$ is part of a straight line (linear pair), so if another angle is known, you can find it by subtracting from $$180^\circ$$.

### Example Scenario:

Suppose angles around point $$ T $$ form a full circle, summing up to $$360^\circ$$. If some angles are given, you can find the unknown angles by subtracting the known angles from $$360^\circ$$.

**For instance:**

- If $$ m \angle PTR = 9^\circ $$ and $$ m \angle PTU = 180^\circ $$, and assuming these angles are adjacent and form part of the full circle around $$ T $$:
  
  $$ m \angle PTR + m \angle PTU + m \angle UTR + m \angle STP = 360^\circ $$
  
  Plug in known values:
  
  $$ 9^\circ + 180^\circ + m \angle UTR + m \angle STP = 360^\circ $$
  
  $$ 189^\circ + m \angle UTR + m \angle STP = 360^\circ $$
  
  $$ m \angle UTR + m \angle STP = 171^\circ $$

From here, additional information or relationships would be needed to solve for $$ m \angle UTR $$ and $$ m \angle STP $$.

### Next Steps:

- **Provide the Diagram:** If possible, share the diagram or describe it in detail. This will allow for more accurate and specific assistance.
  
- **Check the Relationships:** Look for lines that are parallel, perpendicular, or intersecting, and identify any special triangles or polygons that might be present.

- **Use Geometric Theorems:** Apply theorems related to angles, such as the Angle-Sum Theorem, Alternate Interior Angles Theorem, etc., based on the diagram's context.

Feel free to provide more details or the diagram itself, and I'd be happy to help you work through these problems step-by-step!
Cannot determine the answers without the diagram.

tions 17-20, use the diagram of the indicated angle.
17.) 9

18.)
19.)
20.)

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tions 17-20, use the diagram of the indicated angle. 17.) 9 18.) 19.) 20.)