# SOLUTION: The sum of two acute angles is 110. The supplement of the smaller angle is 15 times the complement of the larger angle. What is the measure of the two acute angles? I really don

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 Question 488237: The sum of two acute angles is 110. The supplement of the smaller angle is 15 times the complement of the larger angle. What is the measure of the two acute angles? I really don't get this problem. Please solve this in Elimination Method and please explain. :D THANK YOU in advance to the people who solved this. Answer by Theo(3458)   (Show Source): You can put this solution on YOUR website!the sum of 2 acute angles is 110. the supplement of the smaller angle is 15 times the complement of the larger angle. what is the measure of the 2 acute angles. let the smaller angle be equal to x. let the larger angle be equal to y. you have: x + y = 110 the supplement of the smaller angle is 180 - x. the complement of the larger angle is 90 - y. since the supplement of the smaller angle is 15 times the complement of the larger angle, you also have: (180-x) = 15 * (90-y) the 2 equations that you have to solve simultaneously are: x + y = 110 (first equation) (180-x) = 15 * (90-y) (second equation) we'll solve by substitution. from the first equation, you can solve for y to get: y = 110 - x substitute for y in the second equation to get: (180-x) = 15 * (90 - (110-x)) remove parentheses to get: 180 - x = 15 * (-20 + x) which becomes: 180 - x = -300 + 15x add 300 to both sides of this equation and add x to both sides of this equation to get: 180 + 300 = 15x + x combine like terms to get: 480 = 16x divide both sides of this equation by 16 to get: x = 30 your original equations are: x + y = 110 (first equation) (180-x) = 15 * (90-y) (second equation) substitute for x in the first equation to get: x + y = 110 becomes: 30 + y = 110 solve for y to get: y = 80 your values for x and y are: x = 30 y = 80 to see if these values are good, substitute for x and y in the second equation to get: (180-x) = 15 * (90-y) becomes: (180-30) = 15 * (90-80) which becomes: 150 = 15 * (10) which becomes: 150 = 150 this confirms the values for x and y are good. x is the smaller angle. y is the larger angle. the answer to your question is: the smaller angle is equal to 30 degrees. the larger angle is equal to 80 degrees.