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
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**Title: Finding the Measure of Each Angle in a Quadrilateral**
**Instructions:**
Find the measure of each angle in the given quadrilateral.
**Diagram Description:**
The diagram shows a quadrilateral \(ABCD\) with the following angles provided:
- \(\angle A = 118^\circ\)
- \(\angle C = 78^\circ\)
The vertices are labeled as follows:
- \(A\) at the top-left corner of the quadrilateral.
- \(B\) at the top-right corner.
- \(C\) at the bottom-right corner.
- \(D\) at the bottom-left corner.
**Questions:**
You need to determine the measures of \(\angle B\) (denoted as \(m \angle B\)) and \(\angle D\) (denoted as \(m \angle D\)).
**Formula:**
To find the unknown angles in a quadrilateral, use the fact that the sum of all internal angles in any quadrilateral is \(360^\circ\).
**Step-by-Step Solution:**
1. **Sum of Interior Angles:**
\[
\angle A + \angle B + \angle C + \angle D = 360^\circ
\]
2. **Insert Known Angles:**
\[
118^\circ + \angle B + 78^\circ + \angle D = 360^\circ
\]
3. **Combine the Known Angles:**
\[
118^\circ + 78^\circ = 196^\circ
\]
4. **Set Up the Equation for the Sum of Unknown Angles:**
\[
196^\circ + \angle B + \angle D = 360^\circ
\]
5. **Solve for the Sum of Unknown Angles:**
\[
\angle B + \angle D = 360^\circ - 196^\circ = 164^\circ
\]
Without specific instructions to find the exact measures of \(\angle B\) and \(\angle D\), if additional information or constraints are not given, we can stop here knowing the sum of \(\angle B\) and \(\angle D\) is \(164^\circ\).
**Final Answer:**
- \(m \angle B =\) box for student to fill in
- \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3285f48-0c32-44fd-8ae1-1a69587ed78f%2Ff64d2cfc-59c3-4a16-9e42-1e299628e68b%2Fkev75tk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
**Title: Finding the Measure of Each Angle in a Quadrilateral**
**Instructions:**
Find the measure of each angle in the given quadrilateral.
**Diagram Description:**
The diagram shows a quadrilateral \(ABCD\) with the following angles provided:
- \(\angle A = 118^\circ\)
- \(\angle C = 78^\circ\)
The vertices are labeled as follows:
- \(A\) at the top-left corner of the quadrilateral.
- \(B\) at the top-right corner.
- \(C\) at the bottom-right corner.
- \(D\) at the bottom-left corner.
**Questions:**
You need to determine the measures of \(\angle B\) (denoted as \(m \angle B\)) and \(\angle D\) (denoted as \(m \angle D\)).
**Formula:**
To find the unknown angles in a quadrilateral, use the fact that the sum of all internal angles in any quadrilateral is \(360^\circ\).
**Step-by-Step Solution:**
1. **Sum of Interior Angles:**
\[
\angle A + \angle B + \angle C + \angle D = 360^\circ
\]
2. **Insert Known Angles:**
\[
118^\circ + \angle B + 78^\circ + \angle D = 360^\circ
\]
3. **Combine the Known Angles:**
\[
118^\circ + 78^\circ = 196^\circ
\]
4. **Set Up the Equation for the Sum of Unknown Angles:**
\[
196^\circ + \angle B + \angle D = 360^\circ
\]
5. **Solve for the Sum of Unknown Angles:**
\[
\angle B + \angle D = 360^\circ - 196^\circ = 164^\circ
\]
Without specific instructions to find the exact measures of \(\angle B\) and \(\angle D\), if additional information or constraints are not given, we can stop here knowing the sum of \(\angle B\) and \(\angle D\) is \(164^\circ\).
**Final Answer:**
- \(m \angle B =\) box for student to fill in
- \(
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