Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter1: Variables, Expressions, And Integers
Section1.8: The Coordinate Plane
Problem 2E
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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:**
- \( x = 20 \)
- \( m \angle CAD = 60^\circ \)
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F553a1cb4-91f3-474c-8e72-84014f74b204%2Ff43c31d2-2115-45db-b6fa-5fe8f7c23d74%2Fht0fu2_processed.jpeg&w=3840&q=75)
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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