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Find the values of a and b that would make the quadrilateral a parallelogram. Just type the numbers in the answer boxes.

Find the values of a and b that would make the quadrilateral a parallelogram. Just type the numbers in the answer boxes.

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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Find the values of a and b that would make the quadrilateral a parallelogram.

**Title: Solving for a and b in a Parallelogram** **Objective:** Find the values of \( a \) and \( b \) that make the quadrilateral a parallelogram. **Instructions:** Type the numbers in the answer boxes. **Diagram Explanation:** The image depicts a quadrilateral shape with the interior angles expressed in terms of \( a \) and \( b \): - Top left angle: \( (5b + 6)^\circ \) - Bottom left angle: \( (4a - 8)^\circ \) - Bottom right angle: \( (8a - 10)^\circ \) **Solution Steps:** Since opposite angles in a parallelogram are equal, set the expressions for opposite angles equal to each other: 1. **Equation 1:** \( (5b + 6) = (8a - 10) \) 2. **Equation 2:** \( (4a - 8) = (8a - 10) \) Solve the equations to find the values of \( a \) and \( b \). **Answer Boxes:** - \( a = \) ________ - \( b = \) ________ By solving the equations, you can find the correct values for \( a \) and \( b \) that satisfy the condition of having opposite angles equal, which defines the quadrilateral as a parallelogram.
Transcribed Image Text:**Title: Solving for a and b in a Parallelogram** **Objective:** Find the values of \( a \) and \( b \) that make the quadrilateral a parallelogram. **Instructions:** Type the numbers in the answer boxes. **Diagram Explanation:** The image depicts a quadrilateral shape with the interior angles expressed in terms of \( a \) and \( b \): - Top left angle: \( (5b + 6)^\circ \) - Bottom left angle: \( (4a - 8)^\circ \) - Bottom right angle: \( (8a - 10)^\circ \) **Solution Steps:** Since opposite angles in a parallelogram are equal, set the expressions for opposite angles equal to each other: 1. **Equation 1:** \( (5b + 6) = (8a - 10) \) 2. **Equation 2:** \( (4a - 8) = (8a - 10) \) Solve the equations to find the values of \( a \) and \( b \). **Answer Boxes:** - \( a = \) ________ - \( b = \) ________ By solving the equations, you can find the correct values for \( a \) and \( b \) that satisfy the condition of having opposite angles equal, which defines the quadrilateral as a parallelogram.
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