Final answer:
The sum of the exterior angles of any polygon is always 360 degrees, which is a consistent geometric property used in measuring angles in various contexts, including astronomy. The sum of the exterior angles of any polygon (remember only convex polygons are being discussed here) is 360 degrees. This is a result of the interior angles summing to 180(n-2) degrees and each exterior angle being, by definition, supplementary to its interior angle.
Step-by-step explanation:
The question is regarding the sum of the exterior angle measures of a polygon, which is a mathematical concept in geometry. For any polygon, the sum of its exterior angles is always 360 degrees, no matter how many sides the polygon has. This is a fundamental property that can be observed by extending each side of the polygon in the direction it points and measuring how much you have to turn to draw the next side.
When discussing angles in the sky, astronomers use a different context for angles, but they apply the same principles of geometry to measure positions and movements of celestial bodies. Objects are measured in degrees across the celestial sphere, where 360 degrees make a full circle. For example, the angle the sun covers in the sky from a particular observation point can be measured in degrees, and special instruments like the sextant are used to perform these measurements.
An exterior angle is an angle which is formed by one of the sides of any closed shape structure such as polygon and the extension of its adjacent side. See the figure below, where a five-sided polygon or pentagon is having 5 vertexes. The exterior angles of this pentagon are formed by extending its adjacent sides.