Question 150882: Hello, can you please help me solve this problems:
1.) The sum of the measures of two angles is 180 degrees. Three times the measure of one angle is 24 less than the measure of the other angle. What is the measure of each angle?
2.) The length of a rectangle is 17cm larger than its width. When its width is decreased by 5 cm and its length is increased by 7cm the area of the new rectangle is 22cm² biggerthan the original rectangle. Find the dimension of the original rectangle.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1.) The sum of the measures of two angles is 180 degrees. Three times the measure of one angle is 24 less than the measure of the other angle. What is the measure of each angle?
EQuATIONS:
x + y = 180
3x = y - 24
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Rearrange:
x + y = 180
3x- y = -24
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Add to get:
4x = 156
x = 39 (one of the angles)
Since x+y = 180, the other angle is 180-39 = 141
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2.) The length of a rectangle is 17cm larger than its width. When its width is decreased by 5 cm and its length is increased by 7cm the area of the new rectangle is 22cm² bigger than the original rectangle. Find the dimension of the original rectangle.
EQUATIONS:
L = W + 17
(W-5)(L+7) = LW + 22
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Simplify:
L - W = 17
-5L + 7W = 57
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Rearrange the setup for elimiation:
5L - 5W = 5*17
-5L + 7W = 57
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Add to get:
2W = 5*17+57
W = 71 inches
Since L = W + 17, L = 71+17 = 88 inches
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Cheers,
Stan H.
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