Question

How many different angles would be formed by a transversal intersecting three parallel lines? How many different angle measures would there be?

Answer 1

There would be `12` angles formed by three parallel lines and one traversal.
These angles might be of no more than `2` different measures.

Explanation:

An intersection of two lines forms `4` angles. If one of the is `alpha`, the other three are `beta = 180^o - alpha`, `alpha` and `beta = 180^o - alpha`. So, these four angles are of two different measures.

Exactly the same four angles will be formed by the same traversal and another line, parallel to the first.

Same with the third parallel line.

Altogether we will have 12 angles, but only 2 of them might be different.
If traversal is perpendicular to each of the three lines, we will have only one measure for all angles and it's equal to `90^o`.