Is it possible for a triangle to have angle measurements of 1,2 and 177 degrees?

All triangles have inner angles that add up to 180º.

If they don't add up to 180º, then it's not a triangle.

1 + 2 + 177

3 + 177

180

These three angles add up to 180º, so it IS possible for a triangle to have angles of 1º, 2º, and 177º.