Is it possible for two numbers that are both even to be relatively prime

The definition "relatively prime" is 2 numbers that do not share the same factor. So 2 even numbers, whatever they were, are both dividable by 2, which doesn't make them relatively prime.
Example: 2 and 4, they are both dividable by 2. So they're not relatively prime. Same for 8 and 4, 10 and 16, etc...

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A = 24 + b
c = 4a = 4(24 +b) = 96 + 4b
b =b
a + b + c = 180
24 + b + b + 96 + 4b = 180
Combine the variables and the whole numbers: 
120 + 6b = 180
-120           -120
6b = 60
divide on both sides by 6, and b=10
b = 10 a = 34 c = 136, 10 + 34 + 136 = 180