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19 October, 11:36

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.

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  1. 19 October, 11:56
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    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°
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