Answer:
The answer is: Two
Explanation:
In a convex polygon, the sum of all exterior angles is always 360 degrees. If we assume that all exterior angles are obtuse, each angle contributes more than 90 degrees to the sum. To maximize the number of obtuse angles, we want each exterior angle to be as close as possible to 180 degrees.
For a quadrilateral (four-sided polygon), the maximum number of obtuse exterior angles is two. This occurs when the polygon is concave, and two consecutive exterior angles are close to 180 degrees each. Beyond two obtuse exterior angles, the sum of exterior angles would exceed 360 degrees, violating the properties of a convex polygon. Therefore, two is the maximum number of obtuse exterior angles in a convex polygon.