Lines v and w appear to be parallel in the diagram. Use the angles in ACEF to find what value of x makes v||w. A (3x+25)° (2x+10)° (2х-25)° (x-5) D E B.

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
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Lines V and W appear to be parallel in the diagram. Use angles in CEF to find what value of x makes v||w
**Title:** Understanding Parallel Lines and Angle Relationships

**Introduction:**  
This activity focuses on using angle relationships to determine when two lines are parallel. We will solve for \( x \) to make lines \( v \) and \( w \) parallel using the angles in triangle \( \triangle CEF \).

**Diagram Explanation:**  
In the diagram:

- Lines \( v \) and \( w \) appear to be parallel.
- Points \( A \), \( B \), and \( C \) lie on line \( v \).
- Points \( D \), \( E \), and \( F \) lie on line \( w \).
- Angles are given as follows:
  - Angle \( \angle A \) is labeled as \( (3x + 25)^\circ \).
  - Angle \( \angle B \) is labeled as \( (2x + 10)^\circ \).
  - Angle \( \angle C \) is labeled as \( (2x - 25)^\circ \).
  - Angle \( \angle E \) is labeled as \( (x - 5)^\circ \).

**Task:**  
Use the provided angles to determine the value of \( x \) such that lines \( v \) and \( w \) are parallel.

**Solution Approach:**
To solve for \( x \), we use the property that if the alternate interior angles are equal, then the lines are parallel. Identify the corresponding angles from the diagram and set up the equations to solve for the value of \( x \).

**Your Answer:**
Find the value of \( x \) that satisfies the condition for parallelism in the given triangle and lines.

**Note:** Simplify your answer and do not include the degree symbol in your answer.
Transcribed Image Text:**Title:** Understanding Parallel Lines and Angle Relationships **Introduction:** This activity focuses on using angle relationships to determine when two lines are parallel. We will solve for \( x \) to make lines \( v \) and \( w \) parallel using the angles in triangle \( \triangle CEF \). **Diagram Explanation:** In the diagram: - Lines \( v \) and \( w \) appear to be parallel. - Points \( A \), \( B \), and \( C \) lie on line \( v \). - Points \( D \), \( E \), and \( F \) lie on line \( w \). - Angles are given as follows: - Angle \( \angle A \) is labeled as \( (3x + 25)^\circ \). - Angle \( \angle B \) is labeled as \( (2x + 10)^\circ \). - Angle \( \angle C \) is labeled as \( (2x - 25)^\circ \). - Angle \( \angle E \) is labeled as \( (x - 5)^\circ \). **Task:** Use the provided angles to determine the value of \( x \) such that lines \( v \) and \( w \) are parallel. **Solution Approach:** To solve for \( x \), we use the property that if the alternate interior angles are equal, then the lines are parallel. Identify the corresponding angles from the diagram and set up the equations to solve for the value of \( x \). **Your Answer:** Find the value of \( x \) that satisfies the condition for parallelism in the given triangle and lines. **Note:** Simplify your answer and do not include the degree symbol in your answer.
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