It is given that the angle measures of a triangle are each a multiple of 20. 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
20
20
140
180
Triangle II
20
40
120
180
Triangle III
20
60
100
180
Triangle IV
20
80
80
180
Triangle V
40
40
100
180
Triangle VI
40
60
80
180
Triangle VII
60
60
60
180
As we can see, there are seven possible triangles and only one of them 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=1/7
