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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![The image depicts a pentagon with five interior angles labeled and one side with a variable length "x". The angles are as follows:
- The first angle is 120°.
- The second angle is 90°.
- The third angle is 108°.
- The fourth angle is unknown.
- The fifth angle is 100°.
The side opposite the unknown angle is labeled "x".
To determine the unknown angle, use the formula for the sum of interior angles of a polygon:
\((n-2) \times 180^\circ\),
where \(n\) is the number of sides.
For a pentagon (\(n=5\)), the sum of interior angles is:
\((5-2) \times 180^\circ = 540^\circ\).
To find the unknown angle, subtract the sum of the known angles from 540°:
\[120^\circ + 90^\circ + 108^\circ + 100^\circ = 418^\circ.\]
Therefore, the unknown angle is:
\[540^\circ - 418^\circ = 122^\circ.\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1fb311e-a3e5-4789-a85d-79c6f2a9716e%2F7fb91a67-ca26-4449-9b64-6196104a3dfc%2Fgmjg3w8_processed.png&w=3840&q=75)
Transcribed Image Text:The image depicts a pentagon with five interior angles labeled and one side with a variable length "x". The angles are as follows:
- The first angle is 120°.
- The second angle is 90°.
- The third angle is 108°.
- The fourth angle is unknown.
- The fifth angle is 100°.
The side opposite the unknown angle is labeled "x".
To determine the unknown angle, use the formula for the sum of interior angles of a polygon:
\((n-2) \times 180^\circ\),
where \(n\) is the number of sides.
For a pentagon (\(n=5\)), the sum of interior angles is:
\((5-2) \times 180^\circ = 540^\circ\).
To find the unknown angle, subtract the sum of the known angles from 540°:
\[120^\circ + 90^\circ + 108^\circ + 100^\circ = 418^\circ.\]
Therefore, the unknown angle is:
\[540^\circ - 418^\circ = 122^\circ.\]
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