Explanation:

Let a and b be the two angles in the question, with a>b. We are given that the difference between the angles is 24°.
⇒a–b=24.
Since the average of the two angles is 54°, we have (a+b)/2=54
Solving for b in the first equation yields b=a–24, and substituting this into the second equation yields
a+(a+24)/2=54
(2a−24)/2=54
2a−24=54×2
2a−24=108
2a=108+24
2a=132
a=66
Also, 
b=a−24=66−24=42.
Now, let c be the third angle of the triangle. Since the sum of the angles in the triangle is 180°, 
a+b+c=180. 
Plugging the previous results into the equation yields 66+42+c=180. 
Solving for c yields c=72
Hence, the greatest of the three angles a,b and c is c, which equals 72°