Alan, Bill, and Calvin are playing a game with collectible cards. At the moment, Alan has 11 less than 2 1/2 times the number of
cards Bill has. Calvin has 1 more than 1 1/2 times the number of cards Bill has. If Alan and Calvin have the same number of cards, the number of cards Bill has is ______ . The number of cards Alan and Calvin each have is _____ . If Alan, Bill, and Calvin have all the cards in the deck, then the deck has ____ cards.
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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°
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°