Geometry Question

Since  ∠ABC  and  ∠CBE  form a straight line...

m∠ABC   =   180° - m∠CBE   =   180° - 125°   =   55°

The sum of the angles in a triangle is always  180° , and each angle is greater than  0° , so the sum of any two angles has to be less than 180° . So...

55° + (15x - 92x - 25)°   <   180°

55 + 15x - 92x - 25   <   180

30 - 77x   <   180

-77x   <   150

x   >   - $\frac{150}{77}$

And...

0°  <  (15x - 92x - 25)°

0   <   -77x - 25

25   <   -77x

-$\frac{25}{77}$  >  x

- $\frac{25}{77}$   >   x   >   - $\frac{150}{77}$

All possible values of  x  are in the interval  (-$\frac{150}{77}$, -$\frac{25}{77}$)