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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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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Calculate The Value Of The Variable.
![### Educational Content: Geometric Shapes and Angle Calculations
#### Diagram (c)
This is a diagram of a quadrilateral with labeled angles. The quadrilateral has one right angle (90 degrees) at the bottom right corner. The interior angles are labeled as follows:
- Angle adjacent to the right angle is labeled \( x \).
- The angle directly opposite the right angle is labeled \( 3x \).
- The remaining angle is labeled \( 2x \).
To find the value of \( x \):
We know that the sum of interior angles in any quadrilateral is 360 degrees.
\[ x + 2x + 3x + 90^\circ = 360^\circ \]
\[ 6x + 90^\circ = 360^\circ \]
\[ 6x = 270^\circ \]
\[ x = 45^\circ \]
So, \( x = \) 45 degrees.
---
#### Diagram (d)
This is a pentagon with angles labeled in terms of \( x \). The angles within the pentagon are:
- A right angle (90 degrees) at the top left corner.
- Three angles labeled \( x \) degrees each.
- One angle labeled \( x + 3 \) degrees.
- Additionally, there is an exterior angle labeled 67 degrees.
To find the value of \( x \):
The interior angles of a pentagon sum up to 540 degrees.
\[ 90^\circ + x^\circ + x^\circ + x^\circ + (x + 3)^\circ = 540^\circ \]
\[ 90^\circ + 4x + 3 = 540^\circ \]
\[ 4x + 93^\circ = 540^\circ \]
\[ 4x = 447^\circ \]
\[ x = 111.75^\circ \]
So, \( x = \) 111.75 degrees.
The diagrams help in visualizing the problem and setting up the equations to solve for \( x \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94e3dc3a-5138-4de9-a130-9782421a1710%2Ffe00ee19-5b15-4aaf-a406-7ec1c29a38b4%2Fg075nwg_processed.png&w=3840&q=75)
Transcribed Image Text:### Educational Content: Geometric Shapes and Angle Calculations
#### Diagram (c)
This is a diagram of a quadrilateral with labeled angles. The quadrilateral has one right angle (90 degrees) at the bottom right corner. The interior angles are labeled as follows:
- Angle adjacent to the right angle is labeled \( x \).
- The angle directly opposite the right angle is labeled \( 3x \).
- The remaining angle is labeled \( 2x \).
To find the value of \( x \):
We know that the sum of interior angles in any quadrilateral is 360 degrees.
\[ x + 2x + 3x + 90^\circ = 360^\circ \]
\[ 6x + 90^\circ = 360^\circ \]
\[ 6x = 270^\circ \]
\[ x = 45^\circ \]
So, \( x = \) 45 degrees.
---
#### Diagram (d)
This is a pentagon with angles labeled in terms of \( x \). The angles within the pentagon are:
- A right angle (90 degrees) at the top left corner.
- Three angles labeled \( x \) degrees each.
- One angle labeled \( x + 3 \) degrees.
- Additionally, there is an exterior angle labeled 67 degrees.
To find the value of \( x \):
The interior angles of a pentagon sum up to 540 degrees.
\[ 90^\circ + x^\circ + x^\circ + x^\circ + (x + 3)^\circ = 540^\circ \]
\[ 90^\circ + 4x + 3 = 540^\circ \]
\[ 4x + 93^\circ = 540^\circ \]
\[ 4x = 447^\circ \]
\[ x = 111.75^\circ \]
So, \( x = \) 111.75 degrees.
The diagrams help in visualizing the problem and setting up the equations to solve for \( x \).
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