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.
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°