## Task 4 - 020724

How many different acute exterior angles can a triangle have at most?

Justify your answer!
An exterior angle is as large as the sum of the non-adjacent interior angles.

Assume an exterior angle is acute. Then the two corresponding interior angles together must be less than $90^{\circ}$. This means that the third interior angle is greater than $90^{\circ}$ (sum of interior angles). This angle, being a summand in the other two exterior angles, makes these two greater than $90^{\circ}$. Consequently, a triangle can have at most one acute exterior angle.