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
![### Geometry Problem: Calculating Angle \( m \angle ATL \)
**Problem Statement:**
If \( \overline{AB} \perp \overline{MN} \), \( m \angle ATL = (6x - 12)^\circ \) and \( m \angle LTN = (8x - 24)^\circ \), find \( m \angle ATL \).
**Diagram Explanation:**
The diagram accompanying the problem consists of two perpendicular lines intersecting at point \( T \). The lines are labeled as follows:
- \( \overline{AB} \) is a horizontal line.
- \( \overline{MN} \) is a vertical line intersecting \( \overline{AB} \).
- Point \( T \) is where \( \overline{AB} \) and \( \overline{MN} \) intersect.
- Line \( \overline{LT} \) extends diagonally from \( T \), creating angles with \( \overline{AB} \) and \( \overline{MN} \).
The angles associated with this diagram are:
- \( m \angle ATL \)
- \( m \angle LTN \)
**Choices for the Angle \( m \angle ATL \):**
a. \( 48^\circ \)
b. \( 90^\circ \)
c. \( 42^\circ \)
d. \( 76^\circ \)
### Solution Steps:
1. Given \( \overline{AB} \perp \overline{MN} \), this implies that:
\[ m \angle ATN = 90^\circ \]
2. Since \( \angle ATL \) and \( \angle LTN \) together form the right angle \( \angle ATN \):
\[ m \angle ATL + m \angle LTN = 90^\circ \]
3. Substitute the given expressions for the angles:
\[ (6x - 12)^\circ + (8x - 24)^\circ = 90^\circ \]
4. Combine like terms:
\[ 14x - 36 = 90 \]
5. Solve for \( x \):
\[ 14x = 126 \]
\[ x = 9 \]
6. Substitute \( x = 9 \) back into \( m \angle ATL \):
\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Febcd91cf-c92a-4a76-9c9a-e8d21c0f504d%2Fbf54bf7d-13f4-49ad-89c8-dab283b7e41d%2F4g328bn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometry Problem: Calculating Angle \( m \angle ATL \)
**Problem Statement:**
If \( \overline{AB} \perp \overline{MN} \), \( m \angle ATL = (6x - 12)^\circ \) and \( m \angle LTN = (8x - 24)^\circ \), find \( m \angle ATL \).
**Diagram Explanation:**
The diagram accompanying the problem consists of two perpendicular lines intersecting at point \( T \). The lines are labeled as follows:
- \( \overline{AB} \) is a horizontal line.
- \( \overline{MN} \) is a vertical line intersecting \( \overline{AB} \).
- Point \( T \) is where \( \overline{AB} \) and \( \overline{MN} \) intersect.
- Line \( \overline{LT} \) extends diagonally from \( T \), creating angles with \( \overline{AB} \) and \( \overline{MN} \).
The angles associated with this diagram are:
- \( m \angle ATL \)
- \( m \angle LTN \)
**Choices for the Angle \( m \angle ATL \):**
a. \( 48^\circ \)
b. \( 90^\circ \)
c. \( 42^\circ \)
d. \( 76^\circ \)
### Solution Steps:
1. Given \( \overline{AB} \perp \overline{MN} \), this implies that:
\[ m \angle ATN = 90^\circ \]
2. Since \( \angle ATL \) and \( \angle LTN \) together form the right angle \( \angle ATN \):
\[ m \angle ATL + m \angle LTN = 90^\circ \]
3. Substitute the given expressions for the angles:
\[ (6x - 12)^\circ + (8x - 24)^\circ = 90^\circ \]
4. Combine like terms:
\[ 14x - 36 = 90 \]
5. Solve for \( x \):
\[ 14x = 126 \]
\[ x = 9 \]
6. Substitute \( x = 9 \) back into \( m \angle ATL \):
\
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 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