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A carpenter is building a rectangular bookcase with diagonal braces across the back, as shown. The carpenter knows that mangle ADC is a right angle and that mangle BDC is 31° greater than mangle ADB. Solve an equation to find mangle BDC and mangle ADB.

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abidemiokin

Answer:

Step-by-step explanation:

Let <ADB be x. From the rectangle, <ADB+<BDC = <ADC

<ADB+<BDC = 90° ..... 1

If angle BDC is 31° greater than mangle ADB, then <BDC = x+31

Substituting the given values into the equation 1:

x+x+31 = 90

2x + 31 = 90

2x = 90-31

2x = 59

x = 59/2

x = 29.5°

To get <BDC, we will substitute x = 29.5° into the expression <BDC = x+31

<BDC = 29.5+31

<BDC = 60.5°

Hence <ADB = 29.5° and <BDC = 60.5°

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