Answer: 107 degrees and 73 degrees
107+73 = 180
107-73 = 34
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Step-by-step explanation
Rule: Supplementary angles always add to 180 degrees.
- x+y = 180 is one equation to set up
- x-y = 34 is the other equation since the angles differ by 34 degrees. It's implied here that x > y.
This is our system of equations.
Add the equations straight down.
- x+x = 2x
- y+(-y) = 0y = 0, so the variable y goes away
- 180+34 = 214
After the y terms go away, we have this new equation: 2x = 214 which solves to x = 107 after dividing both sides by 2.
Then use this x value to find y
x+y = 180
107+y = 180
y = 180-107
y = 73
Or you could say
x-y = 34
107-y = 34
-y = 34-107
-y = -73
y = 73
Either way, we get the same y value each time. This helps confirm the answer.
Another way to confirm the answer is shown in the next section below.
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Check:
x+y = 180
107+73 = 180
180 = 180 .... confirms the 1st equation
x-y = 34
107-73 = 34
34 = 34 ... the other equation is confirmed.
In short,