Can a triangle have 2 obtuse outer corners?

If only the two outer corners are obtuse, then the third is sharp. An angle of a triangle adjacent to a given acute angle is necessarily obtuse. The two outer obtuse corners each have an adjacent acute corner.

In total, the triangle has two acute corners and one obtuse one. This is the standard case of an obtuse triangle.

Note: If only one external obtuse angle was required, the situation would be the opposite. The triangle under consideration has two other obtuse angles that are not adjacent to the given one, which is impossible.