Question

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.

Answer 1

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°

Answer 2

1. ∠ADC is right angle, then $m\angle ADC=90^{\circ}.$

2. Angles ADB and BDC are complementary, then

$m\angle ADB+m\angle BDC=m\angle ADC=90^{\circ}.$

3. You know that ∠BDC is 32° greater than ∠ ADB. Let $m\angle ADB=x,$ then $m\angle BDC=x+32^{\circ}.$

Since $m\angle ADB+m\angle BDC=90^{\circ},$ you have that

$x+x+32^{\circ}=90^{\circ},\\ \\2x=90^{\circ}-32^{\circ},\\ \\2x=58^{\circ},\\ \\x=29^{\circ}.$

This gives you:

• $m\angle ADB=29^{\circ};$
• $m\angle BDC=29^{\circ}+32^{\circ}=61^{\circ}.$