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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Question
![**Problem Statement:**
In the figure, \( m \angle ABC = 78^\circ \) and \( m \angle ABD = 32^\circ \). Find the measure of \( x \).
**Diagram Explanation:**
The diagram consists of three points \( A \), \( B \), and \( C \) forming angles at point \( B \). There is also a point \( D \) on the plane of the triangle such that \( \angle ABD = 32^\circ \).
- Point \( A \) is upwards.
- Point \( B \) is at the vertex and to the left.
- Point \( C \) is on the right.
- Point \( D \) is between \( A \) and \( C \).
With these points:
- \( \angle ABC = 78^\circ \)
- \( \angle ABD = 32^\circ \)
- \( \angle DBC = x^\circ \)
**Question:**
What is the measure of \( x \)?
**Multiple Choice Answers:**
- \( 58^\circ \)
- \( 46^\circ \)
- \( 32^\circ \)
- \( 78^\circ \)
**Solution:**
Since angle \( \angle ABC \) is made up of angles \( \angle ABD \) and \( \angle DBC \), we have:
\[
\angle ABC = \angle ABD + \angle DBC
\]
Given, \( \angle ABC = 78^\circ \) and \( \angle ABD = 32^\circ \), so:
\[
78^\circ = 32^\circ + x
\]
Solving for \( x \):
\[
x = 78^\circ - 32^\circ
\]
\[
x = 46^\circ
\]
Therefore, the measure of \( x \) is \( 46^\circ \).
**Answer:**
The correct answer is \( 46^\circ \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F788be1f4-6041-4ab5-a347-ac65fab151c5%2Fbb58c62c-11a3-47de-ba3c-76b2757cc093%2Fw8tjqi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
In the figure, \( m \angle ABC = 78^\circ \) and \( m \angle ABD = 32^\circ \). Find the measure of \( x \).
**Diagram Explanation:**
The diagram consists of three points \( A \), \( B \), and \( C \) forming angles at point \( B \). There is also a point \( D \) on the plane of the triangle such that \( \angle ABD = 32^\circ \).
- Point \( A \) is upwards.
- Point \( B \) is at the vertex and to the left.
- Point \( C \) is on the right.
- Point \( D \) is between \( A \) and \( C \).
With these points:
- \( \angle ABC = 78^\circ \)
- \( \angle ABD = 32^\circ \)
- \( \angle DBC = x^\circ \)
**Question:**
What is the measure of \( x \)?
**Multiple Choice Answers:**
- \( 58^\circ \)
- \( 46^\circ \)
- \( 32^\circ \)
- \( 78^\circ \)
**Solution:**
Since angle \( \angle ABC \) is made up of angles \( \angle ABD \) and \( \angle DBC \), we have:
\[
\angle ABC = \angle ABD + \angle DBC
\]
Given, \( \angle ABC = 78^\circ \) and \( \angle ABD = 32^\circ \), so:
\[
78^\circ = 32^\circ + x
\]
Solving for \( x \):
\[
x = 78^\circ - 32^\circ
\]
\[
x = 46^\circ
\]
Therefore, the measure of \( x \) is \( 46^\circ \).
**Answer:**
The correct answer is \( 46^\circ \).
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