(2x^2+3x-5) & (x^2+11x-7) are supplementary. X? Angle measures?

Since they are supplementary, their sum is 180°.

2x² + 3x - 5  +  x² + 11x - 7  =  180

     3x² + 14x - 12  =  180

     3x² + 14x - 192  =  0

Although this is factorable, it's probably easier to use the quadratic formula:

  x  =  [ -b ±√( b² - 4·a·c ) ] / ( 2·a )   --->   x  =  [ -14 ±√( 14² - 4·3·-192 ) ] / ( 2·3 )

   --->   x  =  [ -14 ±√( 2500 ) ] / ( 6 )   --->  x  =  [ -14 ± 50) ] / ( 6 )   =  6  or  -10 2/3

Place 6 back into the two original quadratic expressions to get the two answers, 85°  and  95°.

The negative answer won't work (try it!).