SOLUTION: Twice the complement of an acute angle exceeds an obtuse angle by 10 degrees. Twice the supplement of the obtuse angle is 15 degrees more than the supplement of the acute angle. Fi

Algebra ->  Angles -> SOLUTION: Twice the complement of an acute angle exceeds an obtuse angle by 10 degrees. Twice the supplement of the obtuse angle is 15 degrees more than the supplement of the acute angle. Fi      Log On


   

Question 668610: Twice the complement of an acute angle exceeds an obtuse angle by 10 degrees. Twice the supplement of the obtuse angle is 15 degrees more than the supplement of the acute angle. Find the acute angle and the obtuse.

I have:
2(90-x)=(90+x)+10
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the acute. Let y be the obtuse.
2(90-x) = y + 10
2(180-y) = (90-x) + 15
180 - 2x = y + 10 --> 170 - 2x = y
360 - 2y = x + 15
360 -2(170-2x) = (90-x)+15
360 - 340 +4x = 105-x
-85 = -5x
x = 17 degrees
170 - 2(17) = y
170 - 34 = 136 degrees
17 degrees - acute
136 degrees - obtuse