A carpenter is building a rectangular bookcase with diagonal braces across the back, as shown. The carpenter knows that angle ADC is a right angle and that m angle BDC is 32degrees greater than m angle ADB. Write and solve an equation to find m angle BDC and m angle ADB.

Question

Mathematics

Elena Rush

18 March, 21:45

A carpenter is building a rectangular bookcase with diagonal braces across the back, as shown. The carpenter knows that angle ADC is a right angle and that m angle BDC is 32degrees greater than m angle ADB. Write and solve an equation to find m angle BDC and m angle ADB.

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Answers (1)

Know the Answer?

Clare Tucker · Answer 1

Refer to the diagram shown below.

Let x = m∠ADB.

Because m∠BDC is 32° greater than m∠ADB, therefore

m∠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°