10. A convex octagon has 8 interior angles.

How many of them, at most, can be right angles?
(A) 4
(B) 2
(C) 3
(D) 5
(E) 1
(10) The correct answer is $(C)$.

For each right interior angle, the exterior angle (which is its supplement) is also right. Since in any convex polygon the sum of the exterior angles is equal to a full angle, it follows that there cannot be more than 3 right angles (unless it is a rectangle, which is to be excluded in the current case). On the other hand, it is not difficult to construct explicit convex polygons with 8 sides having precisely 3 right angles.

Question proposed by Carlo Cassola.