The measure of each angle of a triangle is a multiple of 30°. What is the probability that the triangle has at least two congruent angles?

Well, the triangle could have a few possibilities to get the angles. They are:

30-30-120

30-60-90

30-90-60

30-120-30

60-30-90

60-60-60

60-90-30

90-30-60

90-60-30

Thus, there are 9 possible cases. Out of them 3 are good, so the probability is 1/3, or 33%.