Polygon Exterior Angle Sum Theorem Was Proved By Who?

The Polygon Exterior Angle Sum Theorem states that the sum of all exterior angles in a convex polygon is equal to 360°. This can be proven by considering the sum of interior angles of a polygon, which is given by 180° × n. In any convex polygon with n sides, the sum of the exterior angles always adds up to a full circle (360°). In other words, the total sum of interior and exterior angles of a polygon is 180.

The Polygon Exterior Angle Sum Theorem is Proposition 1.16 in Euclid’s Elements, which states that the measure of an exterior angle of a triangle is greater than either of the measures of the interior angles. Euclid discovered this theorem by drawing figures of certain magnitudes and shapes.

To prove this theorem, consider a polygon with n sides. The sum of the measures of all the exterior angles at each vertex of a convex polygon is 360° (or 4 right angles). The sum of the exterior angles of a polygon having n sides is 180°. The sum of the exterior angles of any polygon is 360 degrees, and an exterior angle of a polygon is the angle that sums to 180°.

In conclusion, the Polygon Exterior Angle Sum Theorem is a fundamental concept in geometry that states that the sum of exterior angles in any polygon adds to 360 degrees.