Exercise 39 Page 177

It is given that the angle measures of a triangle are each a multiple of $12.$ 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 $60^{\circ }.$

Let $m\angle 1,$ $m\angle 2,$ and $m\angle 3$ be the angle measures of the triangles. Let's list all of the possible triangles that satisfy the given requirement. We will start by listing all the triangles with the smallest angle measure of $12.$