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

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2 months ago

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

C 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.

Mathematics

1 answer:

Zina [12.3K] · Answer 1 · 2026-03-07T02:55:59+03:00

Referencing the diagram below, let's denote angle ADB as x. Since angle BDC is 32° more than angle ADB, we can write m∠BDC as x + 32°. Knowing that all angles in a rectangle measure 90°, we set up the equation x + (x + 32) = 90. This simplifies to 2x + 32 = 90, leading to 2x = 58, and then x = 29°. Consequently, angle BDC equals 61°. Therefore, m∠BDC = 61° and m∠ADB = 29°.