Answer:
yes for all 4.
Step-by-step explanation:
I am not sure I see the whole information.
but if the question truly is simply, whether a polygon can have an internal angle of 165 or 171 or 75 or 40 degrees, then the answer is a resounding yes to all 4.
the simplest polygon is a triangle.
the sum of all angles in a triangle is always 180 degrees.
so, any angle smaller than 180 degrees is a possible internal angle in a triangle (and therefore in polygons in general), because the difference to 180 can then be split into 2 angles (e.g. half/half).
so, if one angle is 165 degrees, then the other two angles have to have 15 degrees together (e.g. 10 and 5, or 7 and 8, or 2 and 13, or ...). they will be narrow angles, but they are still angles.
similar for 171 degrees. now the other two angles have to have only 9 degrees together. like 5 and 4.
for 75 degrees the other two angles must have 180-75 = 105 degrees together. like 20 and 85.
for 40 degrees the other two angles must have 180-40 = 140 degrees together. like 90 and 50.
