Using formal Algebra, you can use the sum of interior angles formula:
S = (n - 2)*180
where S = sum of interior angles
n = number of sides
[ You can remember this formula by noting that n-2 is the number
of non-overlapping triangles you can draw by connecting verticies
of an n-sided polygon. Each triangle having 180 degrees. ]
We can compute the average for each of the proposed polygons:
A. quadrilateral: 4 sides --> Sum = (4-2)*180 = 360
Since we are told each angle is obtuse, looking at 360/4 = 90, there
must be some angle that is less than or equal to 90 degrees (allowing
for irregular quadrilaterals). Therefore, this can not be the correct
answer (not all angles can be obtuse).
B. Rectangle: each angle of a rectangle is 90 degrees, clearly not the correct answer. This is already covered by A above as well.
C. Triangle: 3 sides --> Sum = (3-2)*180 = 180 degrees, at most one angle can be obtuse in a triangle, so clearly not the answer.
D. Hexagon: 6 sides: Sum = (6-2)*180 = 720 degrees. Since 720/6 = 120, George must have drawn a hexagon (it doesn't have to be a regular hexagon, BUT it can't be any arbitrary hexagon either, as he must've drawn it such that every angle was obtuse).
In summary, the hexagon shape is the only one possible from the choices given.
Hope this helps you!