SOLUTION: the sum of the measures of an obtuse angle and an acute angle is 160.the sum of the complement of the acute angle ang one-half the supplement of the obtuse angle is 75.find the mea

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Question 326773: the sum of the measures of an obtuse angle and an acute angle is 160.the sum of the complement of the acute angle ang one-half the supplement of the obtuse angle is 75.find the measures of the two angles.
Answer by stanbon(75887) About Me  (Show Source):
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the sum of the measures of an obtuse angle and an acute angle is 160.the sum of the complement of the acute angle ang one-half the supplement of the obtuse angle is 75.find the measures of the two angles
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Let "a" be the obtuse angle and "b" be the acute angle.
Equations:
a + b = 160
(90-b)+(1/2)(180-a) = 75
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Rearrange:
2(90-b) + 180-a = 150
Substitute for "a" and solve for "b":
180-2b + 180-(160-b) = 150
360 -2b -160+b = 150
200 -b = 150
b = 50 degrees
Therefore a = 160-50 = 110 degrees
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Cheers,
Stan H.