SOLUTION: Four times the measure of the complement of an angle is 12 more than twice the difference of the measures of its supplement and its complement. Find the measure of each angle.

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Question 157566: Four times the measure of the complement of an angle is 12 more than twice the difference of the measures of its supplement and its complement. Find the measure of each angle.
Answer by nerdybill(7384) About Me  (Show Source):
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Four times the measure of the complement of an angle is 12 more than twice the difference of the measures of its supplement and its complement. Find the measure of each angle.
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Let x = measure of angle
90-x = complement
180-x = supplement
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4(90-x) = 2((180-x)-(90-x))+12
360-4x = 2(180-x-90+x)+12
360-4x = 2(90)+12
360-4x = 180+12
360-4x = 192
-4x = -168
x = 42 deg (measure of angle)
90-x = 90-42 = 48 deg (measure of complement)
180-x = 180-42 = 138 deg (measure of supplement)