Trigonometry
The calculator finds the missing interior angle of a triangle. You enter two of A, B, and C. The third angle is 180° minus that sum. The steps are short on purpose: this is the first check before the law of sines.
In Euclidean geometry the interior angles of a triangle add to a straight angle. The calculator uses that statement and nothing else. It does not find sides. A zero angle, a negative angle, or two angles that already add to 180° or more cannot describe a triangle.
A = 30° and B = 60°. Find C.
A = 100° and B = 90°. What does the calculator report?
Problem 1. C = 90°.
Problem 2. The two angles already add to 190°, so no third positive angle exists.