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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
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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### 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. \( m = 2, \, n = 7 \)**.
Transcribed Image Text:### 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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