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
find the unknown angles for the figure below
angle b=
angle a=
angle d=
angle e=
angle f=
angle g=
angle h=
![### Transversals and Angle Relationships
**Transversal and Angles Diagram**
In the diagram shown:
- Two parallel horizontal lines are intersected by a transversal, forming eight angles at the points of intersection.
- The angles are labeled as follows:
- At the upper intersection: \( a \), \( b \) as corresponding angles on the horizontal line, and \( d \) as the vertically opposite angle to \( b \).
- At the lower intersection: \( e \), \( f \) as corresponding angles on the horizontal line, and \( g \) and \( h \) as related angles.
The angle relationships provided are:
- \( \angle a = 60^\circ \)
- \( \angle b = 4x - 30^\circ \)
### Analyzing Angle Relationships
1. **Corresponding Angles**: Angles formed on the same side of a transversal with two parallel lines and are equal.
- \( \angle a \) corresponds to \( \angle e \).
- \( \angle b \) corresponds to \( \angle f \).
2. **Alternate Interior Angles**: Angles formed on the opposite sides of a transversal but inside two parallel lines and are equal:
- \( \angle d \) corresponds to \( \angle f \).
- \( \angle e \) corresponds to \( \angle g \).
3. **Alternate Exterior Angles**: Angles formed on the opposite sides of a transversal but outside two parallel lines and are equal:
- \( \angle a \) corresponds to \( \angle h \).
- \( \angle b \) corresponds to \( \angle g \).
4. **Vertically Opposite Angles**: Angles directly opposite each other when two lines intersect and are always equal:
- \( \angle b \) and \( \angle d \) are vertically opposite.
- \( \angle f \) and \( \angle h \) are vertically opposite.
### Solving for \( x \)
To find \( x \) using the given angle relationships:
- Since \( \angle a \) and \( \angle b \) are corresponding angles and the lines are parallel:
\[
\angle a = \angle b
\]
Given:
\[
\angle a = 60^\circ
\]
\[
\angle b = 4x - 30^\circ
\]
thus](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdfc5388e-6899-4768-8712-03421646266d%2F125f3304-7f30-4ccd-9539-b0f663fdd2f8%2Fjs05n97_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Transversals and Angle Relationships
**Transversal and Angles Diagram**
In the diagram shown:
- Two parallel horizontal lines are intersected by a transversal, forming eight angles at the points of intersection.
- The angles are labeled as follows:
- At the upper intersection: \( a \), \( b \) as corresponding angles on the horizontal line, and \( d \) as the vertically opposite angle to \( b \).
- At the lower intersection: \( e \), \( f \) as corresponding angles on the horizontal line, and \( g \) and \( h \) as related angles.
The angle relationships provided are:
- \( \angle a = 60^\circ \)
- \( \angle b = 4x - 30^\circ \)
### Analyzing Angle Relationships
1. **Corresponding Angles**: Angles formed on the same side of a transversal with two parallel lines and are equal.
- \( \angle a \) corresponds to \( \angle e \).
- \( \angle b \) corresponds to \( \angle f \).
2. **Alternate Interior Angles**: Angles formed on the opposite sides of a transversal but inside two parallel lines and are equal:
- \( \angle d \) corresponds to \( \angle f \).
- \( \angle e \) corresponds to \( \angle g \).
3. **Alternate Exterior Angles**: Angles formed on the opposite sides of a transversal but outside two parallel lines and are equal:
- \( \angle a \) corresponds to \( \angle h \).
- \( \angle b \) corresponds to \( \angle g \).
4. **Vertically Opposite Angles**: Angles directly opposite each other when two lines intersect and are always equal:
- \( \angle b \) and \( \angle d \) are vertically opposite.
- \( \angle f \) and \( \angle h \) are vertically opposite.
### Solving for \( x \)
To find \( x \) using the given angle relationships:
- Since \( \angle a \) and \( \angle b \) are corresponding angles and the lines are parallel:
\[
\angle a = \angle b
\]
Given:
\[
\angle a = 60^\circ
\]
\[
\angle b = 4x - 30^\circ
\]
thus
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
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.Similar questions
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