SOLUTION: The sum of the measures of an acute angle and an obtuse angle is 150 degrees. The sum of one- half the measures of the complement of the acute angle angle and five times the measur
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Question 1168829: The sum of the measures of an acute angle and an obtuse angle is 150 degrees. The sum of one- half the measures of the complement of the acute angle angle and five times the measure of the supplement angle of the obtuse angle is 420 degrees . What are the measures of the angle?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The sum of the measures of an acute angle and an obtuse angle is 150 degrees.
A + B = 150
The sum of one-half the measures of the complement of the acute angle angle and five times the measure of the supplement angle of the obtuse angle is 420 degrees
(90-A) + 5(180-B) = 420
45 - .5A + 900 - 5b = 420
-.5A - 5B + 945 = 420
-.5A - 5B = 420 - 945
-.5A - 5B = -525
.5A + 5B = 525, (*-1)
Multiply equation by 2, subtract the first equation
A + 10B = 1050
A + B = 150
------------------------subtraction eliminates A, find B
0 + 9B = 900
B = 900/9
B = 100 degrees is the obtuse angle
therefore
150 - 100 = 50 degrees is the acute angle
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See if that works
"The sum of one-half the measures of the complement of the acute angle angle and five times the measure of the supplement angle of the obtuse angle is 420 "
(90-50) + 5(180-100) = 420
(40) + 5(80) = 420
20 + 400 = 420
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