PLease help me with this! 1. x2 - 9 > 0

2. x2 - 8x + 12 > 0

3. -x2 - 12x - 32 > 0

4. x2 + 3x - 20 >= 3x + 5

1. x2 - 9 > 0

x^2-3^2>0

(x+3)(x-3)>0

(x+3)>0 and (x-3)>0

x>-3       and  x>3

2. x2 - 8x + 12 > 0

   x^2 - 8x  +12>0

   x^2 -2x -6x +12 >0   (-8x is replaced by (-2x) + (-6x) )

   x(x-2) -6(x-2) >0

    (x-6)(x-2)>0

(x-6)>0    and (x-2)>0

    x>6     and     x>2

3. -x2 - 12x - 32 > 0

    -x^2 -12x -32 >0

     x^2 +12x +32 <0

      x^2 +4x +8x +32<0

      x(x+4) +8(x+4)<0

      (x+8)(x+4)<0

(x+8)<0   and  (x+4)<0

x<-8      and    x<-4

4. x2 + 3x - 20 >= 3x + 5

   x^2 +3x -20 >= 3x +5

   x^2 +3x -20 -3x >= 3x +5 -3x

     x^2 -20  >= 5

     x^2 -20 +20  >= 5  +20

     x^2 >=25

     x^2-25 >=0

      (x-5)(x+5)>=0

(x-5)>=0  and (x+5)>=0

  x>=5    and x>=-5

The common angle is the angle that exists in both triangles (pqt and rsq).

Logically, it would be the angle having the same name in both triangles. In our case, it is angle q

Mathematically, we would take a look at both triangles and then get the angle that is found in both.
For example, take a look at the attached picture and comparing the angle in both triangles, we will find that the common angle is angle q