Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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### Solving for \( x \) in Angle Pair Problems Please solve for \( x \). Then circle whether each angle pair is complementary or supplementary. #### Problem 10: Given angles: - \( 5x - 8^\circ \) - \( 43^\circ \) Diagram: - The two angles form a right angle (90 degrees). Solution steps: 1. Determine the equation based on the sum of complementary angles: \( (5x - 8^\circ) + 43^\circ = 90^\circ \) 2. Simplify and solve for \( x \): \( 5x - 8 + 43 = 90 \) \( 5x + 35 = 90 \) \( 5x = 55 \) \( x = 11 \) Verification: - Substitute \( x \) back into the angle equation: \( 5(11) - 8 = 55 - 8 = 47 \) - Check if the angles sum to 90 degrees: \( 47^\circ + 43^\circ = 90^\circ \) Conclusion: - The angle pair is **complementary**. --- #### Problem 11: Given angles: - \( 72^\circ \) - \( 3x + 3^\circ \) Diagram: - The two angles form a right angle (90 degrees). Solution steps: 1. Determine the equation based on the sum of complementary angles: \( 72^\circ + (3x + 3^\circ) = 90^\circ \) 2. Simplify and solve for \( x \): \( 72 + 3x + 3 = 90 \) \( 3x + 75 = 90 \) \( 3x = 15 \) \( x = 5 \) Verification: - Substitute \( x \) back into the angle equation: \( 3(5) + 3 = 15 + 3 = 18 \) - Check if the angles sum to 90 degrees: \( 72^\circ + 18^\circ = 90^\circ \) Conclusion: - The angle pair is **complementary**. ### Angle Types: - **Complementary Angles**: Two angles whose measures sum up to 90 degrees. - **Supplementary Angles**: Two angles whose measures
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Transcribed Image Text:### Solving for \( x \) in Angle Pair Problems Please solve for \( x \). Then circle whether each angle pair is complementary or supplementary. #### Problem 10: Given angles: - \( 5x - 8^\circ \) - \( 43^\circ \) Diagram: - The two angles form a right angle (90 degrees). Solution steps: 1. Determine the equation based on the sum of complementary angles: \( (5x - 8^\circ) + 43^\circ = 90^\circ \) 2. Simplify and solve for \( x \): \( 5x - 8 + 43 = 90 \) \( 5x + 35 = 90 \) \( 5x = 55 \) \( x = 11 \) Verification: - Substitute \( x \) back into the angle equation: \( 5(11) - 8 = 55 - 8 = 47 \) - Check if the angles sum to 90 degrees: \( 47^\circ + 43^\circ = 90^\circ \) Conclusion: - The angle pair is **complementary**. --- #### Problem 11: Given angles: - \( 72^\circ \) - \( 3x + 3^\circ \) Diagram: - The two angles form a right angle (90 degrees). Solution steps: 1. Determine the equation based on the sum of complementary angles: \( 72^\circ + (3x + 3^\circ) = 90^\circ \) 2. Simplify and solve for \( x \): \( 72 + 3x + 3 = 90 \) \( 3x + 75 = 90 \) \( 3x = 15 \) \( x = 5 \) Verification: - Substitute \( x \) back into the angle equation: \( 3(5) + 3 = 15 + 3 = 18 \) - Check if the angles sum to 90 degrees: \( 72^\circ + 18^\circ = 90^\circ \) Conclusion: - The angle pair is **complementary**. ### Angle Types: - **Complementary Angles**: Two angles whose measures sum up to 90 degrees. - **Supplementary Angles**: Two angles whose measures
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