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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![### Problem Statement
Find the measure of ∠g if x ∥ y, \( m∠b = x + 15 \) and \( m∠h = 6x - 10 \).
(Note: The diagram is not to scale.)
### Options
- A. 5
- B. 20
- C. 25
- D. 40
### Diagram Explanation
The diagram features two parallel lines, labeled \( x \) and \( y \), that are intersected by a transversal line. The various angles created by the intersecting lines are labeled as follows:
- Upper left corner: ∠a
- Upper middle (adjacent to ∠a): ∠b
- Upper right corner: ∠c
- Middle right corner (adjacent to ∠c and vertically opposite to ∠g): ∠d
- Lower left corner (vertically opposite to ∠a and adjacent to ∠e): ∠e
- Lower middle (vertically opposite to ∠b): ∠f
- Lower right (vertically opposite to ∠c and adjacent to ∠h): ∠g
- Bottom right corner (adjacent to ∠g and ∠h): ∠h
### Multiple-Choice Answers
- O A
- O B
- O C
- O D
### Steps to Solution
1. Given \( x \parallel y \), we know that the alternate interior angles are congruent.
2. \( m∠b = x + 15 \) and \( m∠h = 6x - 10 \).
3. Since ∠b and ∠h are alternate interior angles, they are equal:
\[ x + 15 = 6x - 10 \]
4. Solve for \( x \):
\[ 15 + 10 = 6x - x \]
\[ 25 = 5x \]
\[ x = 5 \]
5. Substitute \( x \) back into the expression for \( m∠h \):
\[ m∠h = 6(5) - 10 \]
\[ m∠h = 30 - 10 \]
\[ m∠h = 20 \]
6. Therefore, \( m∠g = m∠h = 20 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F492f8302-2af6-4a90-9bdc-ae62d55032ea%2F4f083462-681f-4447-9252-e41c7b35b16b%2Fcevslxo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
Find the measure of ∠g if x ∥ y, \( m∠b = x + 15 \) and \( m∠h = 6x - 10 \).
(Note: The diagram is not to scale.)
### Options
- A. 5
- B. 20
- C. 25
- D. 40
### Diagram Explanation
The diagram features two parallel lines, labeled \( x \) and \( y \), that are intersected by a transversal line. The various angles created by the intersecting lines are labeled as follows:
- Upper left corner: ∠a
- Upper middle (adjacent to ∠a): ∠b
- Upper right corner: ∠c
- Middle right corner (adjacent to ∠c and vertically opposite to ∠g): ∠d
- Lower left corner (vertically opposite to ∠a and adjacent to ∠e): ∠e
- Lower middle (vertically opposite to ∠b): ∠f
- Lower right (vertically opposite to ∠c and adjacent to ∠h): ∠g
- Bottom right corner (adjacent to ∠g and ∠h): ∠h
### Multiple-Choice Answers
- O A
- O B
- O C
- O D
### Steps to Solution
1. Given \( x \parallel y \), we know that the alternate interior angles are congruent.
2. \( m∠b = x + 15 \) and \( m∠h = 6x - 10 \).
3. Since ∠b and ∠h are alternate interior angles, they are equal:
\[ x + 15 = 6x - 10 \]
4. Solve for \( x \):
\[ 15 + 10 = 6x - x \]
\[ 25 = 5x \]
\[ x = 5 \]
5. Substitute \( x \) back into the expression for \( m∠h \):
\[ m∠h = 6(5) - 10 \]
\[ m∠h = 30 - 10 \]
\[ m∠h = 20 \]
6. Therefore, \( m∠g = m∠h = 20 \)
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