Question 362979
I'm a little confused.
Is it 7 more than 1/3 of the second angle squared or is it 7 times more than (1/3) of the second angle squared???
First name your variables.
Let the two angle be A and S.
By definition,
{{{A+S=180}}}
{{{A=7+(1/3)S^2}}}
Substitute,
{{{7+(1/3)S^2+S=180}}}
{{{21+S^2+3S=540}}}
{{{S^2+3S-519=0}}}
Use the quadratic formula,
{{{S = (-3 +- sqrt( 3^2-4*1*(-519) ))/(2*1) }}}
{{{S = (-3 +- sqrt( 9+2076 ))/(2) }}}
{{{S = (-3 +- sqrt( 2085 ))/(2) }}}
Only the positive solution makes sense here,
{{{S = (-3 + sqrt( 2085 ))/(2) }}}
Then,
{{{A+(-3+sqrt(2085))/2=180}}}
{{{A=360/2-(-3+sqrt(2085))/2}}}
{{{A=(363-sqrt(2085))/2}}}
.
.
.
The other way,
{{{A+S=180}}}
{{{A=7(1/3)S^2}}}
Substitute, 
{{{(7/3)S^2+S=180}}}
{{{7S^2+3S=540}}}
{{{7S^2+3S-540=0}}}
You can factor that one,
{{{(7S-60)(S+9)=0}}}
Only the positive solution makes sense here,
{{{7S-60=0}}}
{{{7S=60}}}
{{{S=60/7}}}
Then
{{{A=180-60/7}}}
{{{A=1260/7-60/7}}}
{{{A=1200/7}}}