Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter1: The Six Trigonometric Functions
Section1.2: The Rectangular Coordinate System
Problem 92PS: Draw an angle in standard position whose terminal side contains the point (2, –3). Find the...
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![**Labeling Angles: Understanding Angle Relationships**
In this exercise, you are provided with a geometrical diagram where two parallel lines, \( f \parallel g \), are intersected by a transversal line. The goal is to label each missing angle in the diagram using the given information and your knowledge of angle relationships.
### Diagram Overview:
- **Label Definitions:**
- Parallel lines: \( f \parallel g \)
- Transversal line intersecting both \( f \) and \( g \)
- Given angle: \( 85^\circ \)
- **Angles to Identify:**
- Angle 1
- Angle 2
- Angle 3
- Angle 4
- Angle 5
- Angle 6
- Angle 7
- Angle 8
### Utilizing Angle Relationships:
1. **Corresponding Angles:**
- When a transversal crosses parallel lines, the pairs of corresponding angles are equal.
- Here, angle 2 corresponds to the given \( 85^\circ \), meaning angle 2 is also \( 85^\circ \).
2. **Alternate Interior Angles:**
- Alternate interior angles are equal when the lines are parallel.
- Thus, angle 4 is also \( 85^\circ \).
3. **Vertically Opposite Angles:**
- Vertically opposite angles are equal.
- Therefore, angle 6 is \( 85^\circ \).
4. **Supplementary Angles:**
- Adjacent angles that form a straight line (linear pairs) are supplementary, meaning they add up to \( 180^\circ \).
- Angle 3 (adjacent to \( 85^\circ \)) would be \( 180^\circ - 85^\circ = 95^\circ \).
- Angle 1 (adjacent to angle 3) would also be \( 95^\circ \).
- Angle 7 (vertically opposite to angle 3) would also be \( 95^\circ \).
- Angle 5 (vertically opposite to the given \( 85^\circ \)) is \( 95^\circ \).
- Angle 8 (corresponding to angle 7) is \( 95^\circ \).
### Conclusion:
By using the relationships between angles, we determined the following:
- Angle 1: \( 95^\circ \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0449a0b2-b573-4c37-a73f-7ccfb17fc319%2Fb14ced84-ee52-403f-91a6-96d6c704e68a%2F37wbmec_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Labeling Angles: Understanding Angle Relationships**
In this exercise, you are provided with a geometrical diagram where two parallel lines, \( f \parallel g \), are intersected by a transversal line. The goal is to label each missing angle in the diagram using the given information and your knowledge of angle relationships.
### Diagram Overview:
- **Label Definitions:**
- Parallel lines: \( f \parallel g \)
- Transversal line intersecting both \( f \) and \( g \)
- Given angle: \( 85^\circ \)
- **Angles to Identify:**
- Angle 1
- Angle 2
- Angle 3
- Angle 4
- Angle 5
- Angle 6
- Angle 7
- Angle 8
### Utilizing Angle Relationships:
1. **Corresponding Angles:**
- When a transversal crosses parallel lines, the pairs of corresponding angles are equal.
- Here, angle 2 corresponds to the given \( 85^\circ \), meaning angle 2 is also \( 85^\circ \).
2. **Alternate Interior Angles:**
- Alternate interior angles are equal when the lines are parallel.
- Thus, angle 4 is also \( 85^\circ \).
3. **Vertically Opposite Angles:**
- Vertically opposite angles are equal.
- Therefore, angle 6 is \( 85^\circ \).
4. **Supplementary Angles:**
- Adjacent angles that form a straight line (linear pairs) are supplementary, meaning they add up to \( 180^\circ \).
- Angle 3 (adjacent to \( 85^\circ \)) would be \( 180^\circ - 85^\circ = 95^\circ \).
- Angle 1 (adjacent to angle 3) would also be \( 95^\circ \).
- Angle 7 (vertically opposite to angle 3) would also be \( 95^\circ \).
- Angle 5 (vertically opposite to the given \( 85^\circ \)) is \( 95^\circ \).
- Angle 8 (corresponding to angle 7) is \( 95^\circ \).
### Conclusion:
By using the relationships between angles, we determined the following:
- Angle 1: \( 95^\circ \
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