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
Related questions
Question
![**Educational Content on Parallelograms**
---
**Problem Statement:**
Find \( m∠C \).
---
**Description and Interpretation of the Diagram:**
The given diagram represents a parallelogram \(ABCD\). The vertices are labeled as follows:
- \( A \) and \( D \) form one pair of opposite vertices.
- \( B \) and \( C \) form the other pair of opposite vertices.
In the parallelogram, one of the interior angles between vertices \( A \) and \( D \), labeled as \( ∠D \), measures \( 119° \).
---
**Multiple Choice Options:**
To determine the measure of angle \( ∠C \), the following options are given:
- \( 119 \) degrees
- \( 180 \) degrees
- \( 61 \) degrees
- \( 71 \) degrees
---
**Explanation:**
In a parallelogram, opposite angles are equal, and consecutive angles are supplementary (their measures add up to \( 180° \)).
Given: \( m∠D = 119° \).
Since \( ∠D \) and \( ∠C \) are consecutive angles, they are supplementary.
Therefore:
\[ m∠C + m∠D = 180° \]
\[ m∠C + 119° = 180° \]
Solving for \( m∠C \):
\[ m∠C = 180° - 119° \]
\[ m∠C = 61° \]
Thus, the correct answer is \( 61 \).
**Answer:**
\( 61 \) degrees.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5d29a278-7280-48f4-b81f-861e9ba2f14d%2F12df6214-b752-44de-99e5-4f0388918304%2F24j5oasg_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Content on Parallelograms**
---
**Problem Statement:**
Find \( m∠C \).
---
**Description and Interpretation of the Diagram:**
The given diagram represents a parallelogram \(ABCD\). The vertices are labeled as follows:
- \( A \) and \( D \) form one pair of opposite vertices.
- \( B \) and \( C \) form the other pair of opposite vertices.
In the parallelogram, one of the interior angles between vertices \( A \) and \( D \), labeled as \( ∠D \), measures \( 119° \).
---
**Multiple Choice Options:**
To determine the measure of angle \( ∠C \), the following options are given:
- \( 119 \) degrees
- \( 180 \) degrees
- \( 61 \) degrees
- \( 71 \) degrees
---
**Explanation:**
In a parallelogram, opposite angles are equal, and consecutive angles are supplementary (their measures add up to \( 180° \)).
Given: \( m∠D = 119° \).
Since \( ∠D \) and \( ∠C \) are consecutive angles, they are supplementary.
Therefore:
\[ m∠C + m∠D = 180° \]
\[ m∠C + 119° = 180° \]
Solving for \( m∠C \):
\[ m∠C = 180° - 119° \]
\[ m∠C = 61° \]
Thus, the correct answer is \( 61 \).
**Answer:**
\( 61 \) degrees.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning