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In the diagram below, A is on line segment CE, and line segment AB bisects angle DAC. If  line segment DA is parallel to line segment EF and angle AEF = angle BAC multiplied by 10 and subtracted by 12 degrees, then what is angle DAC in degrees?

 


 

 May 18, 2020
 #1
avatar+111321 
+1

If we  extend FE  in the direction of E to  G ,  then angle  DEG =  180 - AEF  =  180 - (10*BAC - 12)

 

But since DA  is parallel to  EF   this angle  will equal  DAC  =  2 ( BAC)

 

Therefore....this means that

 

2(BAC)  = 180 - (10*BAC - 12)

 

2(BAC)  + (10*BAC - 12)  =   180

 

12BAC  -12   =  180        add 12 to both sides

 

12BAC  =  192     divide  both sides by 12

 

BAC =  16

 

Therfore, angle  DAC  =  2 (BAC)  =   2(16)   =   32°

 

 

cool cool cool

 May 18, 2020
 #2
avatar+692 
+1

Let angle BAC be an  X

 

10X -12 + 2X = 180

 

X = 16   

 

Angle DAC = 2X   wink

 May 18, 2020
edited by Guest  May 18, 2020

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