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
Problem 1CT
Related questions
Topic Video
Question
I’m so confused on how to do this.
![**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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa39f1ceb-7991-4dbf-9368-0145410f7f56%2F1ac72e88-b47f-40a0-86a2-8742e5be2342%2F2cyu9cg_processed.jpeg&w=3840&q=75)
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
∠VRQ = 147o
∠RPQ = 76o
m∠Q = ∠PQR = ?
Step by step
Solved in 2 steps with 1 images

Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Recommended textbooks for you

Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,

Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning

Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,

Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning