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When mZ1 = 75°, d = 43 in., and when mZ1 = 100°, d = 54 in. Neil wants to know how wide a sofa he can buy if he can open the door at most 85°. Using the Hinge Theorem or the Converse of the Hinge Theorem, can you determine the exact value of d when mZ1 85°? If you can, explain the method. If not, explain what you can determine about the distance.

When mZ1 = 75°, d = 43 in., and when mZ1 = 100°, d = 54 in. Neil wants to know how wide a sofa he can buy if he can open the door at most 85°. Using the Hinge Theorem or the Converse of the Hinge Theorem, can you determine the exact value of d when mZ1 85°? If you can, explain the method. If not, explain what you can determine about the distance.

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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When m21 = 75°, d = 43 in., and when mZ1 = 100°, d = 54 in. Neil wants to know how wide a sofa he can buy if he can open the door at most 85°. Using the Hinge Theorem or the Converse of the Hinge Theorem, can you determine the exact value of d when mZ1 = 85°? If you can, explain the method. If not, explain what you can determine about the distance. Choose the correct answer below. The exact value cannot be determined. The Converse of the Hinge Theorem can be used to conclude that when O A. . d> 54, mZ1<100°. The exact value can be determined with the Hinge Theorem. The value is the average of the values of d when 43 + 54 O B. mZ1 = 75° and mZ1= 100°, or = 48.5 in. The exact value can be determined with the Converse of the Hinge Theorem. The value is the solution of the d. 85 or d = 45.9 in. 100 С. proportion 54 The exact value cannot be determined. The Hinge Theorem can be used to conclude that when mZ1= 85°, OD. 43<d<54.
Transcribed Image Text:When m21 = 75°, d = 43 in., and when mZ1 = 100°, d = 54 in. Neil wants to know how wide a sofa he can buy if he can open the door at most 85°. Using the Hinge Theorem or the Converse of the Hinge Theorem, can you determine the exact value of d when mZ1 = 85°? If you can, explain the method. If not, explain what you can determine about the distance. Choose the correct answer below. The exact value cannot be determined. The Converse of the Hinge Theorem can be used to conclude that when O A. . d> 54, mZ1<100°. The exact value can be determined with the Hinge Theorem. The value is the average of the values of d when 43 + 54 O B. mZ1 = 75° and mZ1= 100°, or = 48.5 in. The exact value can be determined with the Converse of the Hinge Theorem. The value is the solution of the d. 85 or d = 45.9 in. 100 С. proportion 54 The exact value cannot be determined. The Hinge Theorem can be used to conclude that when mZ1= 85°, OD. 43<d<54.
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