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In the figure,DC  is parallel to AB .DCA=3x+14  degrees, ACB 10x+12degrees, and CAB=5x-2 degrees. Find the number of degrees in CBA.

 
Guest Aug 10, 2017
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Since DC  is parallel to AB.....angles DCA and CAB will be equal because they are alternate interior angles 

 

So

 

3x + 14  = 5x - 2   subtract  3x from both sides........add 2 to both sides

 

16  = 2x

 

x  = 8

 

And  angles CAB + ACB + CBA  = 180°

 

So  

 

180 - CAB - ACB  =  CBA

 

180 - [ 5(8) - 2 ]  - [ 10 (8) + 12 ]  = CBA   simplify

 

180 - [ 38] - [ 92 ] =  CAB  = 50°

 

 

cool cool cool

 
CPhill  Aug 10, 2017
edited by CPhill  Aug 10, 2017

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