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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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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°

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