### Quadrilateral WXYZ AnalysisThe diagram shows quadrilateral $ WXYZ $. 1. **Side WX:** The expression for side WX is $ 7m + 4 $.2. **Side XY:** The expression for side XY is $ 2n - 1 $.3. **Side YZ:** The expression for side YZ is $ 9m $.4. **Side WZ:** The expression for side WZ is $ n + 6 $. Angles are also given: - **$\angle WXY$:** $ (5y + 13)^\circ $- **$\angle XYZ$:** $ (6y - 8)^\circ $### Parallelogram PropertyFor $ WXYZ $ to be a parallelogram, opposite sides should be equal. Hence,\[ WX = YZ \]\[ XY = WZ \]### Equation Formation1. **Equating $ WX $ and $ YZ $:** \[ 7m + 4 = 9m \] Simplifying this: \[ 4 = 2m \implies m = 2 \]2. **Equating $ XY $ and $ WZ $:** \[ 2n - 1 = n + 6 \] Simplifying this: \[ n - 1 = 6 \implies n = 7 \]**So, the correct values are $ m = 2 $ and $ n = 7 $.**### Multiple Choice Question**What must the values of $ m $ and $ n $ be for $ WXYZ $ to be a parallelogram?**- $ \mathbf{A}. \quad m = 4, \, n = 5 $- $ \mathbf{B}. \quad m = 2, \, n = 7 $- $ \mathbf{C}. \quad m = 18, \, n = 13 $- $ \mathbf{D}. \quad Not enough information $### Correct Answer**B. $ m = 2, \, n = 7 $**.

In parellogram parellel sides are equal So WZ=XY ZY=WX

Quadrilateral WYZ ie shown. 2n-1 (5y 13y 7m + 4 (6y-8y n 6 W What must the values of m and n be for WXYZ to be a parallelogram? O. A. m=4, n= 5. B. m 2, n = 7 C. m=18, n 13 %3D D. not enough information

Quadrilateral WYZ ie shown. 2n-1 (5y 13y 7m + 4 (6y-8y n 6 W What must the values of m and n be for WXYZ to be a parallelogram? O. A. m=4, n= 5. B. m 2, n = 7 C. m=18, n 13 %3D D. not enough information

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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Question

### Quadrilateral WXYZ Analysis

The diagram shows quadrilateral $ WXYZ $.

1. **Side WX:** The expression for side WX is $ 7m + 4 $.
2. **Side XY:** The expression for side XY is $ 2n - 1 $.
3. **Side YZ:** The expression for side YZ is $ 9m $.
4. **Side WZ:** The expression for side WZ is $ n + 6 $.

Angles are also given:

- **$\angle WXY$:** $ (5y + 13)^\circ $
- **$\angle XYZ$:** $ (6y - 8)^\circ $

### Parallelogram Property

For $ WXYZ $ to be a parallelogram, opposite sides should be equal. Hence,

\[ WX = YZ \]
\[ XY = WZ \]

### Equation Formation

1. **Equating $ WX $ and $ YZ $:**
\[
7m + 4 = 9m
\]
Simplifying this:
\[
4 = 2m \implies m = 2
\]

2. **Equating $ XY $ and $ WZ $:**
\[
2n - 1 = n + 6
\]
Simplifying this:
\[
n - 1 = 6 \implies n = 7
\]

**So, the correct values are $ m = 2 $ and $ n = 7 $.**

### Multiple Choice Question

**What must the values of $ m $ and $ n $ be for $ WXYZ $ to be a parallelogram?**

- $ \mathbf{A}. \quad m = 4, \, n = 5 $
- $ \mathbf{B}. \quad m = 2, \, n = 7 $
- $ \mathbf{C}. \quad m = 18, \, n = 13 $
- $ \mathbf{D}. \quad Not enough information $

### Correct Answer

**B. $ m = 2, \, n = 7 $**.

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