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 m angle BDC is 32degrees greater than m angle ADB. Write and solve an equation to find m angle BDC and m angle ADB.

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°