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Use the diagram to find all of the missing angles, knowing that a || b 21 = 42 = 23= 1 3 2 54° 12 11 67° 10 4 7/6 8 9 5 a b

Use the diagram to find all of the missing angles, knowing that a || b 21 = 42 = 23= 1 3 2 54° 12 11 67° 10 4 7/6 8 9 5 a b

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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## Transversals and Angle Measurements Practice ### Instructions: Use the diagram to find all of the missing angles, knowing that \(a \parallel b\). ### Diagram Description: The diagram features two parallel lines, \(a\) and \(b\), which are intersected by two transversals forming various angles. Notable angles include: - \(\angle 3 = 54^\circ\) - \(\angle 8 = 67^\circ\) These angles are used to find the measurements of the other labeled angles in the diagram. ### Labels and Diagram: ``` (arrow a) ------ 1 -- 2 ----------- 4 -- 5 ------------------- (arrow a) | / \ | / \ | 6 / 7 \ 3 \ 54^\circ 67^\circ / 8 | / 10 \ | / \ | 12 / \ 9 | / \ (arrow b) ------ 11 -- 10 --------- 8 -- 9 ---------------- (arrow b) ``` ### Tasks: Determine the following angles: - \(\angle 1\) = \(\_\_\_)^\circ - \(\angle 2\) = \(\_\_\_)^\circ - \(\angle 3\) = \(\_\_\_)^\circ - \(\angle 4\) = \(\_\_\_)^\circ Fill in the boxes with the correct values deduced from the given angles and the properties of parallel lines and transversals. ### Solution Explanation: Using the properties of corresponding angles, alternate interior angles, and vertical angles, explain how you determined the missing angles. Note: The parallel relationship between lines \(a\) and \(b\) is critical to solving for the unknown angles.
Transcribed Image Text:## Transversals and Angle Measurements Practice ### Instructions: Use the diagram to find all of the missing angles, knowing that \(a \parallel b\). ### Diagram Description: The diagram features two parallel lines, \(a\) and \(b\), which are intersected by two transversals forming various angles. Notable angles include: - \(\angle 3 = 54^\circ\) - \(\angle 8 = 67^\circ\) These angles are used to find the measurements of the other labeled angles in the diagram. ### Labels and Diagram: ``` (arrow a) ------ 1 -- 2 ----------- 4 -- 5 ------------------- (arrow a) | / \ | / \ | 6 / 7 \ 3 \ 54^\circ 67^\circ / 8 | / 10 \ | / \ | 12 / \ 9 | / \ (arrow b) ------ 11 -- 10 --------- 8 -- 9 ---------------- (arrow b) ``` ### Tasks: Determine the following angles: - \(\angle 1\) = \(\_\_\_)^\circ - \(\angle 2\) = \(\_\_\_)^\circ - \(\angle 3\) = \(\_\_\_)^\circ - \(\angle 4\) = \(\_\_\_)^\circ Fill in the boxes with the correct values deduced from the given angles and the properties of parallel lines and transversals. ### Solution Explanation: Using the properties of corresponding angles, alternate interior angles, and vertical angles, explain how you determined the missing angles. Note: The parallel relationship between lines \(a\) and \(b\) is critical to solving for the unknown angles.
### Measurement of Angles The following exercise is aimed at helping you practice evaluating the provided angles. You will fill in the boxes with the measured angle in degrees (°). 1. \( \angle 1 \) = [ ]° 2. \( \angle 2 \) = [ ]° 3. \( \angle 3 \) = [ ]° 4. \( \angle 4 \) = [ ]° 5. \( \angle 5 \) = [ ]° 6. \( \angle 6 \) = [ ]° 7. \( \angle 7 \) = [ ]° 8. \( \angle 8 \) = [ ]° 9. \( \angle 9 \) = [ ]° 10. \( \angle 10 \) = [ ]° 11. \( \angle 11 \) = [ ]° 12. \( \angle 12 \) = [ ]° **Instructions:** - Measure each angle using a protractor or an angle-measuring tool. - Record the measured value in the box next to the corresponding angle number. This exercise will aid you in understanding and practicing how to measure and record angles accurately.
Transcribed Image Text:### Measurement of Angles The following exercise is aimed at helping you practice evaluating the provided angles. You will fill in the boxes with the measured angle in degrees (°). 1. \( \angle 1 \) = [ ]° 2. \( \angle 2 \) = [ ]° 3. \( \angle 3 \) = [ ]° 4. \( \angle 4 \) = [ ]° 5. \( \angle 5 \) = [ ]° 6. \( \angle 6 \) = [ ]° 7. \( \angle 7 \) = [ ]° 8. \( \angle 8 \) = [ ]° 9. \( \angle 9 \) = [ ]° 10. \( \angle 10 \) = [ ]° 11. \( \angle 11 \) = [ ]° 12. \( \angle 12 \) = [ ]° **Instructions:** - Measure each angle using a protractor or an angle-measuring tool. - Record the measured value in the box next to the corresponding angle number. This exercise will aid you in understanding and practicing how to measure and record angles accurately.
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