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
![### Solving for x in an Isosceles Trapezoid
**Problem Statement:**
If quadrilateral ABCD is an isosceles trapezoid, find \( x \).
**Diagram:**
Here is a representation of quadrilateral ABCD, which is an isosceles trapezoid:
```
A ____________ D
/ \
/ \
B/_________________\ C
```
- \(\angle B = 65^\circ\)
- \(\angle C = (7x - 26)^\circ\)
**Description:**
In the given quadrilateral ABCD, which is an isosceles trapezoid, we have the following angles:
- \(\angle B = 65^\circ\) is given.
- \(\angle C = (7x - 26)^\circ\) is given in terms of x.
**To Solve for \( x \):**
1. In an isosceles trapezoid, the angles on the same base are supplementary, meaning:
\[
\angle B + \angle C = 180^\circ
\]
2. Substituting the given angles into the equation:
\[
65^\circ + (7x - 26)^\circ = 180^\circ
\]
3. Simplify and solve for \( x \):
\[
65 + 7x - 26 = 180
\]
\[
7x + 39 = 180
\]
\[
7x = 141
\]
\[
x = \frac{141}{7}
\]
\[
x = 20.14
\]
**Answer:**
\( x = 20.14 \)
**Interactive Tools:**
- Calculator interface with number and operation buttons available for solving equations.
- Additional tools for zooming, bookmarking, highlighting, using a line reader, and resetting answers.
This exercise helps in understanding the properties of trapezoids, particularly focusing on the supplementary angles in isosceles trapezoids.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3285f48-0c32-44fd-8ae1-1a69587ed78f%2Ff9d68505-5d0e-4040-a6e5-40ec07f316c5%2Fupyboo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving for x in an Isosceles Trapezoid
**Problem Statement:**
If quadrilateral ABCD is an isosceles trapezoid, find \( x \).
**Diagram:**
Here is a representation of quadrilateral ABCD, which is an isosceles trapezoid:
```
A ____________ D
/ \
/ \
B/_________________\ C
```
- \(\angle B = 65^\circ\)
- \(\angle C = (7x - 26)^\circ\)
**Description:**
In the given quadrilateral ABCD, which is an isosceles trapezoid, we have the following angles:
- \(\angle B = 65^\circ\) is given.
- \(\angle C = (7x - 26)^\circ\) is given in terms of x.
**To Solve for \( x \):**
1. In an isosceles trapezoid, the angles on the same base are supplementary, meaning:
\[
\angle B + \angle C = 180^\circ
\]
2. Substituting the given angles into the equation:
\[
65^\circ + (7x - 26)^\circ = 180^\circ
\]
3. Simplify and solve for \( x \):
\[
65 + 7x - 26 = 180
\]
\[
7x + 39 = 180
\]
\[
7x = 141
\]
\[
x = \frac{141}{7}
\]
\[
x = 20.14
\]
**Answer:**
\( x = 20.14 \)
**Interactive Tools:**
- Calculator interface with number and operation buttons available for solving equations.
- Additional tools for zooming, bookmarking, highlighting, using a line reader, and resetting answers.
This exercise helps in understanding the properties of trapezoids, particularly focusing on the supplementary angles in isosceles trapezoids.
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 6 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.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