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In the figure below, ∠2 = (4? + 10)° and ∠5 = (9? − 25)° and m is parallel to m. a) Find x. b) Find the measure of ∠4

In the figure below, ∠2 = (4? + 10)° and ∠5 = (9? − 25)° and m is parallel to m. a) Find x. b) Find the measure of ∠4

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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In the figure below, ∠2 = (4? + 10)° and ∠5 = (9? − 25)° and m is parallel to m.
a) Find x.
b) Find the measure of ∠4

**Transversal and Angles: Diagram Explanation** In this diagram, we explore the concept of transversals and their interaction with parallel lines. The diagram includes three main lines labeled \( m \), \( n \), and \( k \). The line \( n \) acts as a transversal intersecting lines \( m \) and \( k \). This results in the formation of multiple angles, which are numbered from 1 to 8 in red for identification purposes. ### Description of the Angles 1. **Angle 1**: Formed by the intersection of lines \( n \) and \( m \) on the upper right side. 2. **Angle 2**: Formed on the upper left side where lines \( n \) and \( m \) intersect. 3. **Angle 3**: Adjacent to Angle 1, situated towards the lower left within the same intersection. 4. **Angle 4**: Adjacent to Angle 2, situated towards the lower right within the same intersection. 5. **Angle 5**: Formed by the intersection of lines \( n \) and \( k \) on the upper right side. 6. **Angle 6**: Formed on the upper left side where lines \( n \) and \( k \) intersect. 7. **Angle 7**: Adjacent to Angle 5, lying towards the lower left within the same intersection. 8. **Angle 8**: Adjacent to Angle 6, lying towards the lower right within the same intersection. ### Understanding the Relationships - **Corresponding Angles**: When two parallel lines are cut by a transversal, the angles that occupy the same relative position at each intersection are known as corresponding angles. In this diagram, Angles 1 and 5, Angles 2 and 6, Angles 3 and 7, and Angles 4 and 8 are examples of corresponding angles. - **Alternate Interior Angles**: These are angles that lie between two lines and on opposite sides of the transversal. For instance, Angles 4 and 6, and Angles 3 and 5 are pairs of alternate interior angles. - **Alternate Exterior Angles**: These are angles that lie outside the two lines and on opposite sides of the transversal. In the diagram, Angles 1 and 7, and Angles 2 and 8 represent alternate exterior angles
Transcribed Image Text:**Transversal and Angles: Diagram Explanation** In this diagram, we explore the concept of transversals and their interaction with parallel lines. The diagram includes three main lines labeled \( m \), \( n \), and \( k \). The line \( n \) acts as a transversal intersecting lines \( m \) and \( k \). This results in the formation of multiple angles, which are numbered from 1 to 8 in red for identification purposes. ### Description of the Angles 1. **Angle 1**: Formed by the intersection of lines \( n \) and \( m \) on the upper right side. 2. **Angle 2**: Formed on the upper left side where lines \( n \) and \( m \) intersect. 3. **Angle 3**: Adjacent to Angle 1, situated towards the lower left within the same intersection. 4. **Angle 4**: Adjacent to Angle 2, situated towards the lower right within the same intersection. 5. **Angle 5**: Formed by the intersection of lines \( n \) and \( k \) on the upper right side. 6. **Angle 6**: Formed on the upper left side where lines \( n \) and \( k \) intersect. 7. **Angle 7**: Adjacent to Angle 5, lying towards the lower left within the same intersection. 8. **Angle 8**: Adjacent to Angle 6, lying towards the lower right within the same intersection. ### Understanding the Relationships - **Corresponding Angles**: When two parallel lines are cut by a transversal, the angles that occupy the same relative position at each intersection are known as corresponding angles. In this diagram, Angles 1 and 5, Angles 2 and 6, Angles 3 and 7, and Angles 4 and 8 are examples of corresponding angles. - **Alternate Interior Angles**: These are angles that lie between two lines and on opposite sides of the transversal. For instance, Angles 4 and 6, and Angles 3 and 5 are pairs of alternate interior angles. - **Alternate Exterior Angles**: These are angles that lie outside the two lines and on opposite sides of the transversal. In the diagram, Angles 1 and 7, and Angles 2 and 8 represent alternate exterior angles
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