### Geometry Problem Explanation#### Problem Statement:The image shows a geometric figure with points labeled as $ W, X, Y, $ and $ Z $, forming two intersecting triangles inside a quadrilateral. The following conditions and measurements are provided:1. **Condition**: $ XY = WZ $2. **Angle Measurements**: - $ m\angle 2 = 36^\circ $ - $ m\angle W = 57^\circ $3. **Objective**: Find $ m\angle 3 $#### Diagram Description:The diagram consists of two intersecting triangles within a larger quadrilateral:- **Vertices**: - $W$ on the bottom left of the diagram. - $X$ on the top left of the diagram. - $Y$ on the top right of the diagram. - $Z$ on the bottom right of the diagram.- **Lines and Angles**: - Line segments $WX$, $XY$, $YZ$, and $ZW$. - The quadrilateral forms two triangles $WXY$ and $XYZ$. - Angles within the quadrilateral are labeled as $1, 2, 3,$ and $4$.#### Given Angles:- $ m\angle 2 = 36^\circ $- $ m\angle W = 57^\circ $#### Task:Find the measure of $ \angle 3 $.#### Solution Steps:To find $ m\angle 3 $, follow these logical steps of reasoning involving triangle properties and exterior angles:1. **Triangle $ WXY $**: - Using the given $ m\angle W = 57^\circ $ and $ m\angle 2 = 36^\circ $.2. **Triangle Angle Sum Property**: - The sum of angles in any triangle is $ 180^\circ $. - Therefore, we can write the equation for $ \triangle WXY $: \[ m\angle 1 + m\angle 2 + m\angle W = 180^\circ \] - Substituting the given values: \[ m\angle 1 + 36^\circ + 57^\circ = 180^\circ \] \[ m\angle 1 =

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Description: ### Geometry Problem Explanation#### Problem Statement:The image shows a geometric figure with points labeled as $ W, X, Y, $ and $ Z $, forming two intersecting triangles inside a quadrilateral. The following conditions and measurements are pro

Answered: Image /qna-images/answer/90fe0e56-e1dd-47ab-9a17-c916b257ff5f.jpg

Answered: XY = WZ m22%3D36°, m ZW = 57°, find m23

Math

Geometry

XY = WZ m22%3D36°, m ZW = 57°, find m23

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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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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### Geometry Problem Explanation

#### Problem Statement:
The image shows a geometric figure with points labeled as $ W, X, Y, $ and $ Z $, forming two intersecting triangles inside a quadrilateral. The following conditions and measurements are provided:

1. **Condition**: $ XY = WZ $
2. **Angle Measurements**:
- $ m\angle 2 = 36^\circ $
- $ m\angle W = 57^\circ $
3. **Objective**: Find $ m\angle 3 $

#### Diagram Description:
The diagram consists of two intersecting triangles within a larger quadrilateral:

- **Vertices**:
- $W$ on the bottom left of the diagram.
- $X$ on the top left of the diagram.
- $Y$ on the top right of the diagram.
- $Z$ on the bottom right of the diagram.

- **Lines and Angles**:
- Line segments $WX$, $XY$, $YZ$, and $ZW$.
- The quadrilateral forms two triangles $WXY$ and $XYZ$.
- Angles within the quadrilateral are labeled as $1, 2, 3,$ and $4$.

#### Given Angles:
- $ m\angle 2 = 36^\circ $
- $ m\angle W = 57^\circ $

#### Task:
Find the measure of $ \angle 3 $.

#### Solution Steps:
To find $ m\angle 3 $, follow these logical steps of reasoning involving triangle properties and exterior angles:

1. **Triangle $ WXY $**:
- Using the given $ m\angle W = 57^\circ $ and $ m\angle 2 = 36^\circ $.

2. **Triangle Angle Sum Property**:
- The sum of angles in any triangle is $ 180^\circ $.
- Therefore, we can write the equation for $ \triangle WXY $:
\[
m\angle 1 + m\angle 2 + m\angle W = 180^\circ
\]
- Substituting the given values:
\[
m\angle 1 + 36^\circ + 57^\circ = 180^\circ
\]
\[
m\angle 1 =

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