Can an acute-angled triangle have an acute exterior angle?

Answer 1

No. An interior angle plus its exterior partner add up to 180 degrees.

In order for an exterior angle to be acute, its interior partner would

have to be obtuse, which doesn't happen in an acute triangle.

Answer 2

No, an acute-angled triangle cannot have an acute exterior angle. By definition, an exterior angle of a triangle is formed by extending one of the sides of the triangle. In an acute-angled triangle, all interior angles are less than 90 degrees, so extending any side will create an obtuse exterior angle.