Question

A carpenter is building a rectangular bookcase with diagonal braces across the back, as shown. The

Answer 1

Given that the measure of angle ADC = 90 degrees.
Notice that m<ADC = m<ADB + m<BDC

Let the measure of angle ADB be x degrees, then given that m<BDC is 34 degrees greater than m<ADB, thus, m<BDC = x + 34

Hence,
m<ADC = m<ADB + m<BDC
90 = x + x + 34 = 2x + 34
2x = 90 - 34 = 56
x = 28

Therefore, m<ADB = 28 degrees and m<BDC = 28 + 34 = 62 degrees.