Can you have a convex hexagon with five acute angles?

Question

If you can't, then please explain why!

Answer 1

You cannot. The interior angles of any hexagon sum to 720°. However, if the hexagon has 5 acute angles, the sum of those angles is at most 450°, and since the hexagon is convex, the sixth angle is at most 180°, for a total sum of at most 630°, which is less than the required 720°. Therefore, a convex hexagon cannot have five acute angles.