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A carpenter is building a rectangular bookcase with diagonal braces across the back, as shown. The carpenter knows that ∠ADC is a right angle and that m∠BDC is 32° greater than m∠ADB. Write and solve an
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Jan 22, 2018
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A carpenter is building a rectangular bookcase with diagonal braces across the back, as shown. The carpenter knows that ∠ADC is a right angle and that m∠BDC is 32° greater than m∠ADB. Write and solve an equation to find m∠BDC and m∠ADB
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Mehrad Farahnak
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To solve the problem:
Let x be m ∠ADB.
Because m ∠BDC is 32° greater than m ∠ADB, thereforem ∠BDC = x + 32°
Each angle of a rectangle is 90°, therefore:
x + (x + 32) = 90
2x + 32 = 90
2x = 58
x = 29°
x + 32 = 61°
Answer:
m ∠BDC = 61°
m ∠ADB = 29°
Kaushik Nayak
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Jan 26, 2018
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Kaushik Nayak
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