The sum of the measure of the n interior angles of an n-gon is asn/4
(n-2)*180
triangle sum conjecture is the sum of the measures of the angles in every triangle is 180 degrees
One possible conjecture is that their sum is 27. The conjecture is patently false, but that does not stop it being a conjecture.
The sum of two negative numbers is 27.5 unless you add them together on a Tuesday, in which case the sum is 25.7. That is a conjecture about the sum of two negative numbers. There is no reason for a conjecture to be true, or even credible.
A sphere as a polygon is a shape with three or more sides and a sphere has no sides
A conjecture is an opinion based on incomplete information, or a guess. It need not be true - or even sensible. So my conjecture is that the sum of two fractions is greater than three quarters. That is a nonsensical conjecture, but it is a conjecture and that is what the question requires.
There is no conjecture about the sum of the first 30 positive even numbers. The answer can be derived and proven. A statement that has been proven is no longer a conjecture.
My conjecture is that the sum is 67. A conjecture does not have to be true, or even plausible. You should be able to test it. If it is found to be true then in is no longer a conjecture, if it is found to be false, it is rejected - and so no longer a conjecture. If it cannot be proved either way, it remains a conjecture.
A Regular Polygon
You do not need a conjecture; you can calculate the answer. The answer is 10,100
The sum of the exterior angles of a polygon is 360o.
There is not a general formula for the sum of the sides of an arbitrary polygon.