Final answer:
A triangular polygon with three sides has no exterior angles. A polygon with four sides has two exterior triangles. The number of exterior triangles in a polygon increases by one for each additional side.
Step-by-step explanation:
In order to prove that a triangular polygon has at least two exterior triangles, we can use the fact that the sum of the interior angles of any polygon with n sides is given by (n-2) x 180 degrees. Let's consider a triangular polygon with three sides. The sum of its interior angles is (3-2) x 180 = 180 degrees. Since the sum of the interior angles of a triangle is always 180 degrees, this means that the triangular polygon has no exterior angles.
Now, let's consider a polygon with four sides. The sum of its interior angles is (4-2) x 180 = 360 degrees. Since the sum of the interior angles of a triangle is 180 degrees, this means that the remaining 180 degrees can be split into two angles, creating two exterior triangles.
We can extend this reasoning to polygons with more than four sides. For example, a polygon with five sides will have a sum of interior angles of (5-2) x 180 = 540 degrees. The remaining 360 degrees can be split into three angles, creating three exterior triangles.