### Problem StatementFind 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 ExplanationThe 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 Solution1. 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 $

Name: ### Problem StatementFind the measure of ∠g if x ∥ y, $ m∠b = x + 15
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Description: ### Problem StatementFind 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 ExplanationThe diagram features two parallel lines, labeled \( x \

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Find the measure of 4g if x || y, mzb x+ 15 and mzh 6x - 10. (Note: The diagram is not to scale.) А. 5 В. 20 С. 25 c/d D. 40 a /6 А B.

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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Question

### 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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