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5 The diagram shows two parallel lines cut by a transversal. One angle measure is shown. Find the values of a, b, c, d, e, f, and g. 54° aº Cº bo do eo go

5 The diagram shows two parallel lines cut by a transversal. One angle measure is shown. Find the values of a, b, c, d, e, f, and g. 54° aº Cº bo do eo go

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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### Parallel Lines and Transversals **Question 5:** The diagram shows two parallel lines cut by a transversal. One angle measure is shown as \(54^\circ\). Find the values of angles \(a, b, c, d, e, f, \) and \(g\). **Diagram Explanation:** - The diagram features two parallel lines intersected by a transversal. - The angles surrounding the intersection points are labeled \(a, b, c, d, e, f,\) and \(g\). - One angle is given directly as \(54^\circ\). - Based on angle relationships (such as corresponding angles, alternate interior angles, and vertical angles), calculations can be done to find unknown values. **Angle Relationships to Use:** - **Corresponding Angles:** Angles in corresponding positions between the parallel lines are equal. - **Alternate Interior Angles:** Angles on opposite sides of the transversal but inside the parallel lines are equal. - **Vertical Angles:** Angles that are opposite each other when two lines cross are equal. Use these relationships to solve for each unknown angle.
Transcribed Image Text:### Parallel Lines and Transversals **Question 5:** The diagram shows two parallel lines cut by a transversal. One angle measure is shown as \(54^\circ\). Find the values of angles \(a, b, c, d, e, f, \) and \(g\). **Diagram Explanation:** - The diagram features two parallel lines intersected by a transversal. - The angles surrounding the intersection points are labeled \(a, b, c, d, e, f,\) and \(g\). - One angle is given directly as \(54^\circ\). - Based on angle relationships (such as corresponding angles, alternate interior angles, and vertical angles), calculations can be done to find unknown values. **Angle Relationships to Use:** - **Corresponding Angles:** Angles in corresponding positions between the parallel lines are equal. - **Alternate Interior Angles:** Angles on opposite sides of the transversal but inside the parallel lines are equal. - **Vertical Angles:** Angles that are opposite each other when two lines cross are equal. Use these relationships to solve for each unknown angle.
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