In a triangle, the measure of the first angle is 24 degrees more than the measure of the second angle. the measure of the third angle is four times the measure of the second angle. if the total number of degrees in a triangle is 180, what is the measure of the largest angle? 26 degrees 50 degrees 104 degrees 136 degrees

The first and third angles are expressed in terms of the second angle, so it is convenient to first find its value. Let x represent the second angle. Then we have ..
  first ange = x + 24
  second angle = x
  third angle = 4x
And the sum of angles is
  (x + 24) + (x) + (4x) = 180
  6x +24 = 180
  x = (180 -24)/6 = 26

We can now find the measures of the angles as ...
  first angle = 26 + 24 = 50
  second angle = 26
  third angle = 4*26 = 104

The measure of the largest angle is ...
  104 degrees