Can a triangle be both isosceles and obtuse?

these are two different terms,
isosceles means a triangle with two sides the same length, and hence two angles the same length.
obtuse means there is at least one angle that is greater than 90 degrees.
since two of the angle have to be the same, you know that only one such angle can exist, so is with any triangle anyway.
just try to imagine a triangle with two sides the same length with one angle larger than 90 degrees. yup it's possible