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Label each missing angle in the diagram, using the angle relationships formed knowing f | g. g f 7 5 8 3 #: 65% :: 85 6 1 4 85 :: 957 2 #: 315

Label each missing angle in the diagram, using the angle relationships formed knowing f | g. g f 7 5 8 3 #: 65% :: 85 6 1 4 85 :: 957 2 #: 315

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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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 \
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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