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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.

FreezingTNT  Sep 9, 2018
edited by FreezingTNT  Sep 9, 2018
 #1
avatar+7266 
+1

 

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  (-\(\frac{150}{77}\), -\(\frac{25}{77}\))

hectictar  Sep 10, 2018

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