+92 Triangle ABC has side AB extended in the direction of B to E. m∠CAB = 15x - 92x - 25) and m∠CBE = 125°. Find all possible values of x.
+9466 
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 (-\(\frac{150}{77}\), -\(\frac{25}{77}\))
