It is given that the angle measures of a triangle are each a multiple of 60. We will find the probability that the triangle is equiangular. Recall that an equiangular triangle is a triangle such that all three interior angles are 60^(∘).
Let's list all of the possible triangles that satisfy the given requirement. Let m∠1, m∠2, and m∠3 be the angle measures of the triangles.
Triangles
m∠1
m∠2
m∠3
Sum of the Angles
Triangle I
60
60
60
180
As we can see, there is only one possible triangle and it is equiangular. We can find the probability by dividing the number of favorable outcomes by the number of possible outcomes.
Number of favorable outcomes/Number of possible outcomes=1/1=1
