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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 angle BDC is 32° greater than mangle ADB. Solve an equation to find angle BDC and angle ADB.

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 angle class=

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Answer:

m∠ADB = 29° and m∠BDC = 61°

Step-by-step explanation:

It is given that m∠ADC = 90°

Since m∠ADB + m∠BDC = 90° [∠ADB and ∠BDC are complimentary]

Since ∠BDC = ∠ADB + 32°

So, m∠ADB + m∠ADB + 32° = 90°

2(m∠ADB) + 32° = 90°

2(m∠ADB) = 90 - 32

2(m∠ADB) = 58°

m∠ADB = 29°

Since m∠ADB + m∠BDC = 90°

So, m∠BDC + 29° = 90°

m∠BDC = 90 - 29

             = 61°

Therefore, m∠ADB = 29° and m∠BDC = 61°

m∠ADB = 29° and m∠BDC = 61°

Solving this will just be based on some basic angle theorems in a triangle.

  • We are given; m∠ADB = 29° and m∠BDC = 61°
  •  We are told that m∠ADC is a right angle. This means that; m∠ADC = 90°

  • Now, since m∠ADC = 90°, it means that;

m∠ADB + m∠BDC = 90° (because m∠ADB and m∠BDC are complimentary angles due to the fact that angle at point D is 90°)

  • We are also told that;

m∠BDC is 32° greater than angle m∠ADB

This means that we can write as;

m∠BDC = m∠ADB + 32°

  • From earlier, we saw that;

m∠ADB + m∠BDC = 90°

  • Thus, putting m∠ADB + 32° for m∠BDC, we will have;

m∠ADB + m∠ADB + 32° = 90°

2(m∠ADB) + 32° = 90°

     Subtract 32° from both sides to get;

2(m∠ADB) = 90° - 32°

2(m∠ADB) = 58°

m∠ADB = 58°/2

m∠ADB = 29°

  • Puttting 29° for m∠ADB into; m∠ADB + m∠BDC = 90° gives us;

29° + m∠BDC= 90°

       Subtract 29° from both sides to get;

m∠BDC = 90° - 29°

m∠BDC = 61°

  • In conclusion, m∠ADB = 29° and m∠BDC = 61°

Read more at; brainly.com/question/4687866

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