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Given: L1 || L2 m2 = 132 L2 L1 6. 7 8. 3 4. T1 Give the measure of all the other angles and the reason... Angle Measure Reason 1.

Given: L1 || L2 m2 = 132 L2 L1 6. 7 8. 3 4. T1 Give the measure of all the other angles and the reason... Angle Measure Reason 1.

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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**Transcription and Explanation for Educational Website** **Given Information:** - Lines \( L1 \) are parallel to \( L2 \) (written as \( L1 \parallel L2 \)). - Measure of angle 2 (\( m\angle 2 \)) is \( 132^\circ \). **Diagram Description:** The diagram shows two parallel lines, \( L1 \) and \( L2 \), intersected by a transversal \( T1 \). This creates a series of angles at the intersections. The angles are labeled from 1 to 8. **Task:** Determine the measure of all other angles and provide reasons for each. **Table for Angle Measurements and Reasons:** | Angle | Measure | Reason | |-------|---------|--------------------------------------| | \( \angle 1 \) | \( 48^\circ \) | Supplementary (with \(\angle 2\)) | | \( \angle 2 \) | \( 132^\circ \) | Given | | \( \angle 3 \) | \( 48^\circ \) | Corresponding (with \(\angle 1\)) | | \( \angle 4 \) | \( 132^\circ \) | Vertical (equal to \(\angle 2\)) | | \( \angle 5 \) | \( 48^\circ \) | Corresponding (with \(\angle 3\)) | | \( \angle 6 \) | \( 132^\circ \) | Alternate Interior (with \(\angle 2\)) | | \( \angle 7 \) | \( 48^\circ \) | Vertical (equal to \(\angle 5\)) | | \( \angle 8 \) | \( 132^\circ \) | Supplementary (with \(\angle 5\)) | **Explanation:** - **Supplementary Angles:** Two angles that add up to \( 180^\circ \). - **Vertical Angles:** Angles opposite each other when two lines cross; they are always equal. - **Corresponding Angles:** Angles that are in the same position at each intersection where a transversal crosses parallel lines; they are equal. - **Alternate Interior Angles:** Angles that are on opposite sides of the transversal and inside the two lines; when the lines are parallel, these angles are
Transcribed Image Text:**Transcription and Explanation for Educational Website** **Given Information:** - Lines \( L1 \) are parallel to \( L2 \) (written as \( L1 \parallel L2 \)). - Measure of angle 2 (\( m\angle 2 \)) is \( 132^\circ \). **Diagram Description:** The diagram shows two parallel lines, \( L1 \) and \( L2 \), intersected by a transversal \( T1 \). This creates a series of angles at the intersections. The angles are labeled from 1 to 8. **Task:** Determine the measure of all other angles and provide reasons for each. **Table for Angle Measurements and Reasons:** | Angle | Measure | Reason | |-------|---------|--------------------------------------| | \( \angle 1 \) | \( 48^\circ \) | Supplementary (with \(\angle 2\)) | | \( \angle 2 \) | \( 132^\circ \) | Given | | \( \angle 3 \) | \( 48^\circ \) | Corresponding (with \(\angle 1\)) | | \( \angle 4 \) | \( 132^\circ \) | Vertical (equal to \(\angle 2\)) | | \( \angle 5 \) | \( 48^\circ \) | Corresponding (with \(\angle 3\)) | | \( \angle 6 \) | \( 132^\circ \) | Alternate Interior (with \(\angle 2\)) | | \( \angle 7 \) | \( 48^\circ \) | Vertical (equal to \(\angle 5\)) | | \( \angle 8 \) | \( 132^\circ \) | Supplementary (with \(\angle 5\)) | **Explanation:** - **Supplementary Angles:** Two angles that add up to \( 180^\circ \). - **Vertical Angles:** Angles opposite each other when two lines cross; they are always equal. - **Corresponding Angles:** Angles that are in the same position at each intersection where a transversal crosses parallel lines; they are equal. - **Alternate Interior Angles:** Angles that are on opposite sides of the transversal and inside the two lines; when the lines are parallel, these angles are
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