Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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what is the value of X 
![The image displays a geometric diagram on graph paper and involves parallel lines and a triangle.
- The diagram consists of two parallel lines, labeled \( a \) and \( b \), and a triangle that intersects these lines.
- The angles of the triangle are labeled as \( x \), \( y \), and \( z \).
- Line \( a \) is parallel to line \( b \), indicated by \( a \parallel b \).
- The angle measurements given are \( y = 45^\circ \) and \( z = 53^\circ \).
- The question posed is: "What is the value of \( x \)?"
To solve, recognize that since \( a \parallel b \), the angles \( y \), \( z \), and \( x \) are related through the properties of parallel lines and transversals. Specifically, angle \( x \) and angle \( y \) are alternate interior angles, and angle \( z \) forms a linear pair with angle \( x \).
Knowing the angle sum property of a triangle (sum of interior angles is \( 180^\circ \)), you can solve for \( x \) using:
\[ x + y + z = 180^\circ \]
Substitute the given values:
\[ x + 45^\circ + 53^\circ = 180^\circ \]
\[ x = 180^\circ - 98^\circ \]
\[ x = 82^\circ \]
Thus, the value of \( x \) is \( 82^\circ \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faac6dbee-0fa3-4cab-9895-bede2017bf0f%2Ffd20a1f0-c962-4589-ab89-a49ca9ba6f5e%2F8qivrft_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image displays a geometric diagram on graph paper and involves parallel lines and a triangle.
- The diagram consists of two parallel lines, labeled \( a \) and \( b \), and a triangle that intersects these lines.
- The angles of the triangle are labeled as \( x \), \( y \), and \( z \).
- Line \( a \) is parallel to line \( b \), indicated by \( a \parallel b \).
- The angle measurements given are \( y = 45^\circ \) and \( z = 53^\circ \).
- The question posed is: "What is the value of \( x \)?"
To solve, recognize that since \( a \parallel b \), the angles \( y \), \( z \), and \( x \) are related through the properties of parallel lines and transversals. Specifically, angle \( x \) and angle \( y \) are alternate interior angles, and angle \( z \) forms a linear pair with angle \( x \).
Knowing the angle sum property of a triangle (sum of interior angles is \( 180^\circ \)), you can solve for \( x \) using:
\[ x + y + z = 180^\circ \]
Substitute the given values:
\[ x + 45^\circ + 53^\circ = 180^\circ \]
\[ x = 180^\circ - 98^\circ \]
\[ x = 82^\circ \]
Thus, the value of \( x \) is \( 82^\circ \).
Expert Solution
Step 1
We know that sum of three angle of a triangle is 180°
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Solved in 2 steps with 1 images
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