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a f C/d g 121°

a f C/d g 121°

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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The image shows a geometry problem involving two parallel lines and a transversal. The question is: 1. If line \( m \parallel n \), which statement is true? ### Diagram Details: - Two parallel lines, \( m \) and \( n \), are intersected by a transversal. - The angles formed are labeled as \( a \), \( b \), \( c \), \( d \), \( e \), \( f \), and \( g \). - Angle \( g \) is specified as \( 121^\circ \). ### Explanation: When a transversal crosses parallel lines, corresponding angles are equal, alternate interior angles are equal, and consecutive interior angles are supplementary. Here is a breakdown of the angles: - \( \angle g = 121^\circ \) - Corresponding angle to \( \angle g \) is \( \angle b \) (also \( 121^\circ \)). - Alternate interior to \( \angle g \) is \( \angle e \). - Angles \( \angle g \) and \( \angle f \) are supplementary (\( \angle g + \angle f = 180^\circ \)). The solution requires identifying true statements regarding these relationships.
Transcribed Image Text:The image shows a geometry problem involving two parallel lines and a transversal. The question is: 1. If line \( m \parallel n \), which statement is true? ### Diagram Details: - Two parallel lines, \( m \) and \( n \), are intersected by a transversal. - The angles formed are labeled as \( a \), \( b \), \( c \), \( d \), \( e \), \( f \), and \( g \). - Angle \( g \) is specified as \( 121^\circ \). ### Explanation: When a transversal crosses parallel lines, corresponding angles are equal, alternate interior angles are equal, and consecutive interior angles are supplementary. Here is a breakdown of the angles: - \( \angle g = 121^\circ \) - Corresponding angle to \( \angle g \) is \( \angle b \) (also \( 121^\circ \)). - Alternate interior to \( \angle g \) is \( \angle e \). - Angles \( \angle g \) and \( \angle f \) are supplementary (\( \angle g + \angle f = 180^\circ \)). The solution requires identifying true statements regarding these relationships.
In the diagram, two intersecting lines form various angles labeled as \( a, b, c, d, e, f, \) and \( g \). A known angle \( \angle d \) measures 121°. Next to the diagram, there is a multiple-choice question with the following options: - \( m \angle c = 59^\circ \) - \( m \angle e = 121^\circ \) - Vertical angles are supplementary - \( m \angle f = 121^\circ \) The diagram illustrates the concept of vertical angles and linear pairs, where certain angles are congruent or supplementary based on their positions relative to each other.
Transcribed Image Text:In the diagram, two intersecting lines form various angles labeled as \( a, b, c, d, e, f, \) and \( g \). A known angle \( \angle d \) measures 121°. Next to the diagram, there is a multiple-choice question with the following options: - \( m \angle c = 59^\circ \) - \( m \angle e = 121^\circ \) - Vertical angles are supplementary - \( m \angle f = 121^\circ \) The diagram illustrates the concept of vertical angles and linear pairs, where certain angles are congruent or supplementary based on their positions relative to each other.
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