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
![The image displays a quadrilateral labeled as WXYZ. The angles of the quadrilateral are as follows:
- Angle at vertex X is 100°.
- Angle at vertex Y is 130°.
- Angle at vertex Z is 66°.
- Angle at vertex W is marked as \(x^\circ\).
To find the value of \(x\), we use the fact that the sum of the interior angles of a quadrilateral is 360°. Therefore, the equation is:
\[ 100^\circ + 130^\circ + 66^\circ + x^\circ = 360^\circ \]
Solving for \(x\):
\[ 296^\circ + x^\circ = 360^\circ \]
\[ x^\circ = 360^\circ - 296^\circ \]
\[ x^\circ = 64^\circ \]
Thus, the angle at vertex W (\(x\)) is 64°.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa2828bc8-b047-40e2-bc26-f48bf2586489%2F7e50d0d0-74d2-4b23-885b-b7cd629b2289%2F6hp2a3i_processed.png&w=3840&q=75)
Transcribed Image Text:The image displays a quadrilateral labeled as WXYZ. The angles of the quadrilateral are as follows:
- Angle at vertex X is 100°.
- Angle at vertex Y is 130°.
- Angle at vertex Z is 66°.
- Angle at vertex W is marked as \(x^\circ\).
To find the value of \(x\), we use the fact that the sum of the interior angles of a quadrilateral is 360°. Therefore, the equation is:
\[ 100^\circ + 130^\circ + 66^\circ + x^\circ = 360^\circ \]
Solving for \(x\):
\[ 296^\circ + x^\circ = 360^\circ \]
\[ x^\circ = 360^\circ - 296^\circ \]
\[ x^\circ = 64^\circ \]
Thus, the angle at vertex W (\(x\)) is 64°.
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