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?
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
