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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![### Geometry Problem 12.1.B-8
#### Problem Statement:
Congruent sides are marked on the figure to the right. Find the values of \(x\) and \(y\).
#### Diagram Description:
The given diagram is a geometric figure composed of two triangles, \( \triangle ABD \) and \( \triangle BCD \). Points \( A \), \( B \), \( C \), and \( D \) are the vertices of these triangles.
- Sides \( AD \) and \( BD \) are marked as congruent (each denoted by a single dash).
- Sides \( BD \) and \( DC \) are also marked as congruent (each denoted by a single dash).
Angles \( \angle BAD \) and \( \angle DBC \) are both marked as \(x^\circ\).
Angle \( \angle DCB \) is marked as \( y^\circ \).
#### Questions:
Determine the values of:
- \( x \)
- \( y \)
#### Answer:
\[
x = \boxed{\,\,\ \,\,^\circ}
\]
\[
y = \boxed{\,\,\ \,\,^\circ}
\]
### Solution Steps:
1. Identify the properties of congruent triangles and the relationships between their angles.
2. Use the angle sum property of triangles to set up equations for \( x \) and \( y \).
3. Solve the equations to find the values of \( x \) and \( y \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0244785f-fcaa-4950-8f5a-3a439b94046c%2Feb04b4d4-4cac-49f3-9d8a-55ab6bdd684f%2Fk3k9pmk_processed.png&w=3840&q=75)
Transcribed Image Text:### Geometry Problem 12.1.B-8
#### Problem Statement:
Congruent sides are marked on the figure to the right. Find the values of \(x\) and \(y\).
#### Diagram Description:
The given diagram is a geometric figure composed of two triangles, \( \triangle ABD \) and \( \triangle BCD \). Points \( A \), \( B \), \( C \), and \( D \) are the vertices of these triangles.
- Sides \( AD \) and \( BD \) are marked as congruent (each denoted by a single dash).
- Sides \( BD \) and \( DC \) are also marked as congruent (each denoted by a single dash).
Angles \( \angle BAD \) and \( \angle DBC \) are both marked as \(x^\circ\).
Angle \( \angle DCB \) is marked as \( y^\circ \).
#### Questions:
Determine the values of:
- \( x \)
- \( y \)
#### Answer:
\[
x = \boxed{\,\,\ \,\,^\circ}
\]
\[
y = \boxed{\,\,\ \,\,^\circ}
\]
### Solution Steps:
1. Identify the properties of congruent triangles and the relationships between their angles.
2. Use the angle sum property of triangles to set up equations for \( x \) and \( y \).
3. Solve the equations to find the values of \( x \) and \( y \).
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