In triangle abc, m∠abc = (4x – 12)° and m∠acb = (2x + 26)°. yin says that if x = 19, the triangle must be equilateral. is he correct? justify your answer

He is not correct.  If this is to be an equilateral triangle then all the angles must be the same measure.  That means that 180/3 = 60°.  They all have to equal 60°.  If one of the angles measures 4x-12, then 4x-12=60.  Solving for x, we will add 12 to both sides to get 4x=72.  x here is 18.  For the other angle measuring 2x+26, we would do the same.  2x+26=60.  Subtract 26 from both sides to get 2x= 34 and x = 17.  He was way off.