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
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help me please!
![**Trapezoid Problem: Solving for x**
Given that each figure is a trapezoid, solve for \( x \).
**Description:**
In the trapezoid \( ABCD \):
- The angles at vertices \( D \) and \( C \) are given.
- The angle at vertex \( C \) is \( 110^\circ \).
- The angle at vertex \( D \) is expressed as \( 11x + 15 \).
**Task:**
To find the value of \( x \) that satisfies the trapezoid angle condition.
**Explanation:**
In any trapezoid, the sum of consecutive angles between the parallel sides is \( 180^\circ \). Thus, we use the following equation:
\[ 11x + 15 + 110 = 180 \]
Simplify and solve for \( x \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e449208-cf4f-4e53-8cac-e5c4c8cafa96%2Fcf0e7f79-bc3f-41fe-b3dc-594e338f42f2%2Fyusdrif_processed.png&w=3840&q=75)
Transcribed Image Text:**Trapezoid Problem: Solving for x**
Given that each figure is a trapezoid, solve for \( x \).
**Description:**
In the trapezoid \( ABCD \):
- The angles at vertices \( D \) and \( C \) are given.
- The angle at vertex \( C \) is \( 110^\circ \).
- The angle at vertex \( D \) is expressed as \( 11x + 15 \).
**Task:**
To find the value of \( x \) that satisfies the trapezoid angle condition.
**Explanation:**
In any trapezoid, the sum of consecutive angles between the parallel sides is \( 180^\circ \). Thus, we use the following equation:
\[ 11x + 15 + 110 = 180 \]
Simplify and solve for \( x \).
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