A convex, 11-sided polygon can have at most how many acute interior angles?
A convex, 11-sides polygon (known as a hendecagon) may only have, at most, 3 acute interior angles.
This is because each acute angle results in an exterior angle that is greater than 90 degrees. If you were to add a fourth exterior angle, the sum of all the exterior angles will be greater than 360 degrees. Of course, the sum of all the exterior angles in a convex polygon must be equal to 360, so if the sum of all are greater than this number, you can cannot create a convex polygon.