Can you sketch an obtuse equiangular triangle?

No, I can't. No such thing can exist.

-- The interior angles of every triangle add up to 180 degrees.

-- An obtuse triangle is one with an angle greater than 90 degrees in it.

-- An equiangular triangle is one with all 3 angles the same size.

If one of them is obtuse, then they're all obtuse.

-- Three times (more than 90 degrees) = (more than 270 degrees).

Not possible.

-- So an obtuse equiangular triangle can't exist.