Do you remember from high school geometry the proof that the sum of the interior angles of a triangle equals 180°, half a circle ?

It is quite simple. We extend each of the three sides of the triangle at one end of the side so that there is one extension at each corner of the triangle.

At each corner the extended side with its extension makes a straight angle, 180°, a half circle, as the dashed arcs in the figure. The total of those three straight angles for the three corners of the triangle is 3 times the ½ circle, 180°, of each for 1½ circles, 540° total.

If one imagines standing in the triangle and facing in direction "A", then turning to the left to face direction "B", then turning further left to direction "C", and then continuing turning left until again facing direction "A", one would have turned through one full circle, 360°.

The three turns were through the three exterior angles, the dotted arcs in the figure.

Each (dashed) straight angle is the sum of an interior angle plus one of the (dotted) exterior angles turned through.

Since the three straight angles total 1½ circles, 540°, and the exterior angles total 1 circle, 360°, then the interior angles must total the difference, ½ circle, 180°.

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Science has always been empirical, the observation of behavior then the hypothesizing, inferring, of the law of behavior that is apparently being followed.