Question

1. exterior angle sum theorem: for any polygon (no triangles), explain why its constant, and show a visual of the exterior turns.
2. real - world example: at least one real - world connection (architecture, stop sign, soccer ball, etc.)

Explanation:

The exterior - angle sum theorem for polygons states that the sum of the exterior angles of any polygon is always 360°. For a triangle, each exterior angle is equal to the sum of the two non - adjacent interior angles. When we sum all three exterior angles of a triangle, we get 360°. In real - world examples, in architecture, the angles at corners of structures are related to polygon angles. A stop sign is an octagon, and the exterior angles help in its design for visibility and shape. A soccer ball has a pattern of polygons on its surface, and the exterior angles are relevant to its geometric construction.

Answer:

The exterior - angle sum of a polygon is 360° because of the geometric relationships between interior and exterior angles. Real - world examples include architecture, stop signs, and soccer balls.