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

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) (Show Source): You can put this solution on YOUR website!
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
-----------------------------------
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.
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