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Find the value of a and measure of the angles. C 6xº 3x⁰ B A D m/CAD = HE * m/CAB= m/BAD-

Find the value of a and measure of the angles. C 6xº 3x⁰ B A D m/CAD = HE * m/CAB= m/BAD-

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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### Geometry Problem: Finding Angle Measures **Problem Statement:** Find the value of \( x \) and measure the angles. **Diagram Explanation:** The diagram shown is composed of four points labeled \( A \), \( B \), \( C \), and \( D \). Line segments \( AB \) and \( AD \) form an angle at point \( A \). There are three angles with the following labeled measures: - Angle \( CAB \) is labeled as \( 6x^\circ \). - Angle \( CAD \) is labeled as \( 3x^\circ \). Points \( A \), \( B \), \( C \), and \( D \) are arranged such that: - \( B \) and \( D \) are on a straight line passing through \( A \). - Point \( C \) is above this straight line forming the additional angles with lines \( AB \) and \( AD \). **Answer Section:** - \( x = \_\_\_ \) - \( m \angle CAD = \_\_\_ \) - \( m \angle CAB = \_\_\_ \) - \( m \angle BAD = \_\_\_ \) **Solution Steps:** 1. Recognize that the angles \( CAB \) and \( CAD \) are adjacent angles that together form a straight line with angle \( BAD \). Therefore, the sum of angle \( CAB \) and angle \( CAD \) should equal \( 180^\circ \). 2. Set up the equation: \[ 6x^\circ + 3x^\circ = 180^\circ \] 3. Solve for \( x \): \[ 9x^\circ = 180^\circ \] \[ x = 20^\circ \] 4. Substitute \( x \) back into the expressions for each angle: - \( m \angle CAD = 3x = 3 \times 20^\circ = 60^\circ \) - \( m \angle CAB = 6x = 6 \times 20^\circ = 120^\circ \) - \( m \angle BAD = 180^\circ \) (since \( B \), \( A \), and \( D \) are on a straight line) **Final Answers:** - \( x = 20 \) - \( m \angle CAD = 60^\circ \) -
Transcribed Image Text:### Geometry Problem: Finding Angle Measures **Problem Statement:** Find the value of \( x \) and measure the angles. **Diagram Explanation:** The diagram shown is composed of four points labeled \( A \), \( B \), \( C \), and \( D \). Line segments \( AB \) and \( AD \) form an angle at point \( A \). There are three angles with the following labeled measures: - Angle \( CAB \) is labeled as \( 6x^\circ \). - Angle \( CAD \) is labeled as \( 3x^\circ \). Points \( A \), \( B \), \( C \), and \( D \) are arranged such that: - \( B \) and \( D \) are on a straight line passing through \( A \). - Point \( C \) is above this straight line forming the additional angles with lines \( AB \) and \( AD \). **Answer Section:** - \( x = \_\_\_ \) - \( m \angle CAD = \_\_\_ \) - \( m \angle CAB = \_\_\_ \) - \( m \angle BAD = \_\_\_ \) **Solution Steps:** 1. Recognize that the angles \( CAB \) and \( CAD \) are adjacent angles that together form a straight line with angle \( BAD \). Therefore, the sum of angle \( CAB \) and angle \( CAD \) should equal \( 180^\circ \). 2. Set up the equation: \[ 6x^\circ + 3x^\circ = 180^\circ \] 3. Solve for \( x \): \[ 9x^\circ = 180^\circ \] \[ x = 20^\circ \] 4. Substitute \( x \) back into the expressions for each angle: - \( m \angle CAD = 3x = 3 \times 20^\circ = 60^\circ \) - \( m \angle CAB = 6x = 6 \times 20^\circ = 120^\circ \) - \( m \angle BAD = 180^\circ \) (since \( B \), \( A \), and \( D \) are on a straight line) **Final Answers:** - \( x = 20 \) - \( m \angle CAD = 60^\circ \) -
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