If angle A+angle B +angle C = (180 degrees) ,-A=B+C

Mmm

$$\\\pi-A=B+C\;\rightarrow\;A=\pi-(B+C)\\ or\\ A=B+C$$

But I can add 2pi*n to these answers where n is an integer

$$\\A=\pi-(B+C)+2n\pi=(2n+1)\pi-(B+C)\\ or\\ A=B+C +2n\pi$$

Mmm

$$\\A=(2n+1)\pi-(B+C)\\ or\\ A=2n\pi+(B+C)\\\\\\\\ $I think the general formula for this would be$\\ A=(-1)^n(B+C)+n\pi$$

I think that is right but I really need another mathematician to check my working.  :))

A+B+C = Pi

B + C    =  Pi - A

cos(B +C)= cos (Pi -A)

cos (B+C) = -(cos A)

-(cos A) = cos(-A)

so that,

cos(B +C)   = cos(-A)

now we cut cos

B+C    = -A//