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
![### Finding Missing Angle Measures in Polygons
For each of the following polygons, calculate the missing angle measures.
#### a. Pentagon
- **Given Angles:** 113°, 52°, 133°, 80°
- **Missing Angle:** x
To find the missing angle, use the formula for the sum of the interior angles of a polygon:
\[
\text{Sum of interior angles} = (n-2) \times 180^\circ
\]
where \(n\) is the number of sides. For a pentagon (\(n = 5\)):
\[
\text{Sum} = (5-2) \times 180^\circ = 540^\circ
\]
Calculate the missing angle:
\[
x + 113^\circ + 52^\circ + 133^\circ + 80^\circ = 540^\circ
\]
\[
x + 378^\circ = 540^\circ
\]
\[
x = 162^\circ
\]
#### b. Quadrilateral
- **Given Angles:** \(x + 32^\circ\), 90°, \(x - 12^\circ\)
- **Missing Angle:** x
Use the sum formula for a quadrilateral (\(n = 4\)):
\[
\text{Sum} = (4-2) \times 180^\circ = 360^\circ
\]
Calculate \(x\):
\[
(x + 32^\circ) + 90^\circ + (x - 12^\circ) + 90^\circ = 360^\circ
\]
\[
2x + 200^\circ = 360^\circ
\]
\[
2x = 160^\circ
\]
\[
x = 80^\circ
\]
#### c. Hexagon
- **Given Angles:** 130°, 120°, \(x + 5^\circ\), \(x + 5^\circ\)
- **Missing Angle:** x
Use the sum formula for a hexagon (\(n = 6\)):
\[
\text{Sum} = (6-2) \times 180^\circ = 720^\circ
\]
Calculate \(x\):
\[
130^\circ + 120^\circ + (x + 5^\circ) + (x + 5^\circ) + (x + 5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04492ec3-6172-46f3-8627-4051d5f516e8%2Ff639fc81-da1d-469b-bc65-ea9df3d48aa3%2Fprh0g6c_processed.png&w=3840&q=75)
Transcribed Image Text:### Finding Missing Angle Measures in Polygons
For each of the following polygons, calculate the missing angle measures.
#### a. Pentagon
- **Given Angles:** 113°, 52°, 133°, 80°
- **Missing Angle:** x
To find the missing angle, use the formula for the sum of the interior angles of a polygon:
\[
\text{Sum of interior angles} = (n-2) \times 180^\circ
\]
where \(n\) is the number of sides. For a pentagon (\(n = 5\)):
\[
\text{Sum} = (5-2) \times 180^\circ = 540^\circ
\]
Calculate the missing angle:
\[
x + 113^\circ + 52^\circ + 133^\circ + 80^\circ = 540^\circ
\]
\[
x + 378^\circ = 540^\circ
\]
\[
x = 162^\circ
\]
#### b. Quadrilateral
- **Given Angles:** \(x + 32^\circ\), 90°, \(x - 12^\circ\)
- **Missing Angle:** x
Use the sum formula for a quadrilateral (\(n = 4\)):
\[
\text{Sum} = (4-2) \times 180^\circ = 360^\circ
\]
Calculate \(x\):
\[
(x + 32^\circ) + 90^\circ + (x - 12^\circ) + 90^\circ = 360^\circ
\]
\[
2x + 200^\circ = 360^\circ
\]
\[
2x = 160^\circ
\]
\[
x = 80^\circ
\]
#### c. Hexagon
- **Given Angles:** 130°, 120°, \(x + 5^\circ\), \(x + 5^\circ\)
- **Missing Angle:** x
Use the sum formula for a hexagon (\(n = 6\)):
\[
\text{Sum} = (6-2) \times 180^\circ = 720^\circ
\]
Calculate \(x\):
\[
130^\circ + 120^\circ + (x + 5^\circ) + (x + 5^\circ) + (x + 5
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