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
help me please!
![**Problem: Solve for \( x \).**
The diagram is a pentagon with the interior angles labeled as follows:
- Top left angle: \( 85^\circ \)
- Top angle: \( 115^\circ \)
- Top right angle: \( 95^\circ \)
- Bottom right angle: \( x \)
- Bottom left angle: \( 130^\circ \)
**Explanation:**
To solve for \( x \), we need to use the formula for the sum of the interior angles of a pentagon.
The sum of the interior angles of a polygon is given by:
\[
\text{Sum} = (n-2) \times 180^\circ
\]
where \( n \) is the number of sides. For a pentagon, \( n = 5 \).
So, the sum of the interior angles is:
\[
(5-2) \times 180^\circ = 3 \times 180^\circ = 540^\circ
\]
Now, let's set up the equation using the given angles:
\[
85^\circ + 115^\circ + 95^\circ + 130^\circ + x = 540^\circ
\]
Adding these angles:
\[
425^\circ + x = 540^\circ
\]
Subtracting \( 425^\circ \) from both sides:
\[
x = 540^\circ - 425^\circ = 115^\circ
\]
Therefore, \( x = 115^\circ \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e449208-cf4f-4e53-8cac-e5c4c8cafa96%2F64a7d600-9947-4ed1-8035-4085f40c4af8%2Fa6hsizp_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem: Solve for \( x \).**
The diagram is a pentagon with the interior angles labeled as follows:
- Top left angle: \( 85^\circ \)
- Top angle: \( 115^\circ \)
- Top right angle: \( 95^\circ \)
- Bottom right angle: \( x \)
- Bottom left angle: \( 130^\circ \)
**Explanation:**
To solve for \( x \), we need to use the formula for the sum of the interior angles of a pentagon.
The sum of the interior angles of a polygon is given by:
\[
\text{Sum} = (n-2) \times 180^\circ
\]
where \( n \) is the number of sides. For a pentagon, \( n = 5 \).
So, the sum of the interior angles is:
\[
(5-2) \times 180^\circ = 3 \times 180^\circ = 540^\circ
\]
Now, let's set up the equation using the given angles:
\[
85^\circ + 115^\circ + 95^\circ + 130^\circ + x = 540^\circ
\]
Adding these angles:
\[
425^\circ + x = 540^\circ
\]
Subtracting \( 425^\circ \) from both sides:
\[
x = 540^\circ - 425^\circ = 115^\circ
\]
Therefore, \( x = 115^\circ \).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
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