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
Question
100%
![**Title: Solving Angles in a Geometric Diagram**
**Instructions:**
Solve for \( x \) and then list the three angle measures.
**Diagram Explanation:**
The image contains a geometric diagram with three angles originating from a common point, resembling a triangle. These angles are denoted as:
- \( (x+3)^\circ \)
- \( (x-1)^\circ \)
- \( (x+1)^\circ \)
The sum of the angles in such a construction totals 90 degrees as they seem to form a right angle with the horizontal baseline.
**Objective:**
To find the value of \( x \) by solving the equation based on the angle sum and then calculate the measure of each angle.
**Equation:**
\[
(x+3) + (x-1) + (x+1) = 90
\]
**Steps to Solve:**
1. Combine like terms in the equation:
\[
3x + 3 = 90
\]
2. Subtract 3 from both sides:
\[
3x = 87
\]
3. Divide by 3:
\[
x = 29
\]
**Angle Measures:**
1. \( (x+3)^\circ = (29+3)^\circ = 32^\circ \)
2. \( (x-1)^\circ = (29-1)^\circ = 28^\circ \)
3. \( (x+1)^\circ = (29+1)^\circ = 30^\circ \)
These calculations verify the angle measures as parts of a right angle configuration.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9dfbebbf-8e50-4299-b8dd-04968c79c6a1%2F473357a6-d5aa-408d-9dad-13825c782a9d%2Fen7fpw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Solving Angles in a Geometric Diagram**
**Instructions:**
Solve for \( x \) and then list the three angle measures.
**Diagram Explanation:**
The image contains a geometric diagram with three angles originating from a common point, resembling a triangle. These angles are denoted as:
- \( (x+3)^\circ \)
- \( (x-1)^\circ \)
- \( (x+1)^\circ \)
The sum of the angles in such a construction totals 90 degrees as they seem to form a right angle with the horizontal baseline.
**Objective:**
To find the value of \( x \) by solving the equation based on the angle sum and then calculate the measure of each angle.
**Equation:**
\[
(x+3) + (x-1) + (x+1) = 90
\]
**Steps to Solve:**
1. Combine like terms in the equation:
\[
3x + 3 = 90
\]
2. Subtract 3 from both sides:
\[
3x = 87
\]
3. Divide by 3:
\[
x = 29
\]
**Angle Measures:**
1. \( (x+3)^\circ = (29+3)^\circ = 32^\circ \)
2. \( (x-1)^\circ = (29-1)^\circ = 28^\circ \)
3. \( (x+1)^\circ = (29+1)^\circ = 30^\circ \)
These calculations verify the angle measures as parts of a right angle configuration.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 1 images
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