Find mZQ for the diagram in degrees. 147° R. 76

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
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**Title: Calculating the Measure of an Angle in a Diagram**

**Problem Statement:**
Find \( m\angle Q \) for the diagram in degrees.

**Diagram Explanation:**
The diagram is a triangle \( \triangle PQR \) with an external line segment \( \overline{RV} \). The known angles in the diagram are:
- \( \angle VRP = 147^\circ \)
- \( \angle QPR = 75^\circ \)

The task is to determine the measure of the angle \( \angle Q \).

**Solution:**
In \( \triangle PQR \), the sum of the internal angles is always \( 180^\circ \). We can use the following equation:

1. Sum of internal angles: 
   \[
   \angle P + \angle Q + \angle R = 180^\circ
   \]

2. We know:
   \[
   \angle P = 75^\circ
   \]
   \[
   \angle VRP = 147^\circ \quad (\text{external angle to } \angle R)
   \]

3. Using the external angle theorem:
   \[
   \angle VRP = \angle Q + \angle P
   \]
   \[
   147^\circ = \angle Q + 75^\circ
   \]

4. Solving for \( \angle Q \):
   \[
   \angle Q = 147^\circ - 75^\circ = 72^\circ
   \]

**Final Answer:**
\( m\angle Q = 72^\circ \)

**Submit your work using the form:**

- **Answer:** [Input Box]
- Click [Submit Answer] to check your response.
Transcribed Image Text:**Title: Calculating the Measure of an Angle in a Diagram** **Problem Statement:** Find \( m\angle Q \) for the diagram in degrees. **Diagram Explanation:** The diagram is a triangle \( \triangle PQR \) with an external line segment \( \overline{RV} \). The known angles in the diagram are: - \( \angle VRP = 147^\circ \) - \( \angle QPR = 75^\circ \) The task is to determine the measure of the angle \( \angle Q \). **Solution:** In \( \triangle PQR \), the sum of the internal angles is always \( 180^\circ \). We can use the following equation: 1. Sum of internal angles: \[ \angle P + \angle Q + \angle R = 180^\circ \] 2. We know: \[ \angle P = 75^\circ \] \[ \angle VRP = 147^\circ \quad (\text{external angle to } \angle R) \] 3. Using the external angle theorem: \[ \angle VRP = \angle Q + \angle P \] \[ 147^\circ = \angle Q + 75^\circ \] 4. Solving for \( \angle Q \): \[ \angle Q = 147^\circ - 75^\circ = 72^\circ \] **Final Answer:** \( m\angle Q = 72^\circ \) **Submit your work using the form:** - **Answer:** [Input Box] - Click [Submit Answer] to check your response.
Expert Solution
Step 1

Geometry homework question answer, step 1, image 1

∠VRQ = 147o 

∠RPQ = 76o

m∠Q = ∠PQR = ?  

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