# A tricky math problem. pls help!?

Question:the sum of the measure of an obtuse angle and an acute angle is 160. the sum of the complement of the acute angle and one-half the supplement of the obtuse angle is 75. Find the measures of the 2 angles.

Supposedly, our teacher told us to solve it using one variable. I can't figure it out. Please help. If you do know the answer, please include an explanation. Thanks!

Let x be the acute angle and 160-x be the obtuse angle
and (90-x) be the complement of the acute angle and (180-(160-x)) be the supplement of the obtuse angle. Then the equation would be:
(90-x)+1/2(180-(160-x))=75
90-x +1/2(180-160+x)=75
90-x+1/2(20+x)=75
90-x+10+x/2=75 =>Multiply by the LCD 2
180-2x + 20 + x = 150
200-x=150
x=50

Then the acute angle is 50 and the obtuse angle is 110.
Hope this helps..
x + y = 160
(90-x) + 1/2(180-y) = 75

i have no idea how you can get it by using only one variable. if you use TWO variables, though, you'll get at the system of equations written above, where x is the acute angle and y is the obtuse angle.
solving for x and y, you'll get
x = 160 - y
sunstitute this into the second example, and eliminate the fraction:
2(90 - 160 + y) + (180 - y) = 2(75)
2y - 140 + 180 - y = 150
y = 110
x = 50
why bother to use one variable? In math, you should use the easier way around.
There should be 2 equations:
x+y =160
(90-x) + 1/2y = 75

so now, u substitute..if u like or use the process of elimination but i prefer substituting so:
it will be x = 160 - y
so substituting to equation 2: u get
90-(160-y) + 1/2y = 75
90-160+y +1/2y = 75
-70 +3/2y = 75
3/2y = 145
y =96.7

x = 160 -96.7
x = 63.3

Complement = 2 angles that add to 90deg
Supplement = 2 angles that add to 180deg

acute < 90 deg
180 > obtuse > 90

now to get this into something managable...
A + O = 160 <----- 1st Equation

(90 - A) + 1/2(180 - O) = 75
-A -1/2O = -105
A + 1/2O = 105 <----- 2nd Equation

now using simultaneous equations you can work it out;
Equation 1 - Equation 2
1/2O = 55
O = 110 deg

Enter O into either Equation 1 or Equation 2 to find A;
A + 1/2O = 105
A + 1/2(110) = 105
A + 55 = 105
A = 50 deg

Simple ^_^
Well if the sum of the both the angles is 160 then lets say
x + y = 160
and y = 160 - x
The sum of the complement and half the supplement is 75 which means
(180 - y/2) + 90 - x = 75
Therefore:
75 = 270 - (160 - x) / 2 - x
= 190 - 1.5x
-115 = -1.5x
that means the value of the acute angle is 76 and 2/3 you stick that in the formula of the obtuse angle which gives you the value of 83 and 1/3
I thinks thats right

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