Using the diagram below, identify the relationship between the given angles and then find the value of x that makes m || n. X₂ (2x − 95)° to The given angles are X =
Using the diagram below, identify the relationship between the given angles and then find the value of x that makes m || n. X₂ (2x − 95)° to The given angles are X =
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Trigonometry
Section1.8: Applications And Models
Problem 4ECP: From the time a small airplane is 100 feet high and 1600 ground feet from its landing runway, the...
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![### Understanding Angle Relationships
#### Task:
Using the diagram below, identify the relationship between the given angles and then find the value of \( x \) that makes \( m \parallel n \).
#### Diagram Explanation:
In the diagram, two lines \( m \) and \( n \) are shown. There is a transversal line intersecting \( m \) and \( n \) forming the following angles:
- Angle labeled \( (2x - 95)^\circ \)
- Angle labeled \( x^\circ \)
These angles are positioned such that their relationship can determine whether lines \( m \) and \( n \) are parallel.
### Problem:
- **Given Angles:** Identify the angles and their relationship.
- **Calculate \( x \):** Find the value of \( x \) that makes \( m \parallel n \).
#### Calculation:
Explain the steps to find the relationship and the specific value of \( x \) ensuring \( m \parallel n \).
1. **Identify Angles:**
- \( (2x - 95)^\circ \)
- \( x^\circ \)
2. **Relationship Exploration:**
- To satisfy the condition \( m \parallel n \), corresponding angles, alternate interior angles, or other angle relationships that guarantee parallel lines need to be identified and equated.
3. **Solving for \( x \):**
- Use the appropriate angle relationship to set up an equation.
- Solve the equation to find the value of \( x \).
### Example Calculation:
Consider that for \( m \parallel n \), the following relationship might hold for alternate interior angles or corresponding angles:
- \( (2x - 95)^\circ = x^\circ \)
- Solve for \( x \).
\[ 2x - 95 = x \]
\[ 2x - x = 95 \]
\[ x = 95 \]
Therefore, if \( x = 95 \), then \( m \parallel n \).
### Conclusion:
After solving, input your answer:
**The given angles are** [Fill in relationship type, e.g., alternate interior angles, corresponding angles, etc.]
**\( x \) =** [Answer]
### Interactive Element:
- Dropdown or input box for users to input the value of \( x \).
By understanding the angle relationships and solving for \( x \), students will grasp the concept of parallel lines intersected by a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0449a0b2-b573-4c37-a73f-7ccfb17fc319%2F19005d64-0174-484a-8f1c-4af597957606%2Fhswnh99_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Angle Relationships
#### Task:
Using the diagram below, identify the relationship between the given angles and then find the value of \( x \) that makes \( m \parallel n \).
#### Diagram Explanation:
In the diagram, two lines \( m \) and \( n \) are shown. There is a transversal line intersecting \( m \) and \( n \) forming the following angles:
- Angle labeled \( (2x - 95)^\circ \)
- Angle labeled \( x^\circ \)
These angles are positioned such that their relationship can determine whether lines \( m \) and \( n \) are parallel.
### Problem:
- **Given Angles:** Identify the angles and their relationship.
- **Calculate \( x \):** Find the value of \( x \) that makes \( m \parallel n \).
#### Calculation:
Explain the steps to find the relationship and the specific value of \( x \) ensuring \( m \parallel n \).
1. **Identify Angles:**
- \( (2x - 95)^\circ \)
- \( x^\circ \)
2. **Relationship Exploration:**
- To satisfy the condition \( m \parallel n \), corresponding angles, alternate interior angles, or other angle relationships that guarantee parallel lines need to be identified and equated.
3. **Solving for \( x \):**
- Use the appropriate angle relationship to set up an equation.
- Solve the equation to find the value of \( x \).
### Example Calculation:
Consider that for \( m \parallel n \), the following relationship might hold for alternate interior angles or corresponding angles:
- \( (2x - 95)^\circ = x^\circ \)
- Solve for \( x \).
\[ 2x - 95 = x \]
\[ 2x - x = 95 \]
\[ x = 95 \]
Therefore, if \( x = 95 \), then \( m \parallel n \).
### Conclusion:
After solving, input your answer:
**The given angles are** [Fill in relationship type, e.g., alternate interior angles, corresponding angles, etc.]
**\( x \) =** [Answer]
### Interactive Element:
- Dropdown or input box for users to input the value of \( x \).
By understanding the angle relationships and solving for \( x \), students will grasp the concept of parallel lines intersected by a
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