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
![### Geometry Problem: Finding Angle Measures
#### Problem Statement:
In the diagram below, \( \overline{AB} \parallel \overline{CD} \), \( \overline{AD} \parallel \overline{BC} \), \( \overline{AD} \cong \overline{AE} \), and \( m \angle C = 72^\circ \). Find \( m \angle DEB \).
#### Diagram:
The diagram features a quadrilateral with vertices labeled A, B, C, and D. There is an additional point E on the line segment AD such that \( AD \parallel BC \) and \( \overline{AD} \parallel \overline{AE} \). The angle at vertex C, \( \angle C \), is marked as \( 72^\circ \).
- \( \overline{AB} \) is parallel to \( \overline{CD} \).
- \( \overline{AD} \) is parallel to \( \overline{BC} \).
- \( \overline{AD} \cong \overline{AE} \).
#### Calculation Objective:
Determine the measure of \( \angle DEB \).
You may assume lines that appear straight are straight, but the figure is not otherwise drawn to scale.
#### Solution Input:
\[ \text{Answer: } m \angle DEB = \_\_\_\_ ^\circ \]
Teacher's Note: This exercise is aimed at practicing the use of parallel lines and congruent segments to find unknown angles in geometric figures. Students should apply concepts of parallel lines and transversals, as well as the properties of congruent triangles, to arrive at the correct solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93e35ee3-d6cc-41bd-8e16-f9ac42c71034%2F86434d10-1781-4c11-84c3-b75d311c780d%2Fiuvx1o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometry Problem: Finding Angle Measures
#### Problem Statement:
In the diagram below, \( \overline{AB} \parallel \overline{CD} \), \( \overline{AD} \parallel \overline{BC} \), \( \overline{AD} \cong \overline{AE} \), and \( m \angle C = 72^\circ \). Find \( m \angle DEB \).
#### Diagram:
The diagram features a quadrilateral with vertices labeled A, B, C, and D. There is an additional point E on the line segment AD such that \( AD \parallel BC \) and \( \overline{AD} \parallel \overline{AE} \). The angle at vertex C, \( \angle C \), is marked as \( 72^\circ \).
- \( \overline{AB} \) is parallel to \( \overline{CD} \).
- \( \overline{AD} \) is parallel to \( \overline{BC} \).
- \( \overline{AD} \cong \overline{AE} \).
#### Calculation Objective:
Determine the measure of \( \angle DEB \).
You may assume lines that appear straight are straight, but the figure is not otherwise drawn to scale.
#### Solution Input:
\[ \text{Answer: } m \angle DEB = \_\_\_\_ ^\circ \]
Teacher's Note: This exercise is aimed at practicing the use of parallel lines and congruent segments to find unknown angles in geometric figures. Students should apply concepts of parallel lines and transversals, as well as the properties of congruent triangles, to arrive at the correct solution.
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