To classify triangle DEF according to its angle measures, we need to use the fact that the sum of the angles in a triangle is always 180 degrees.
E(2x+11), D(4x+7), and F(7x-3) are the angles of triangle DEF.
(2x+11) + (4x+7) + (7x-3) = 180
13x + 15 = 180
13x = 165
x = 165/13
x = 12.69 (rounded to two decimal places)
Now we can find the measures of each angle:
E = 2x+11 = 2(12.69)+11 = 36.38 degrees
D = 4x+7 = 4(12.69)+7 = 59.88 degrees
F = 7x-3 = 7(12.69)-3 = 85.83 degrees
Since all three angles are less than 90 degrees, triangle DEF is an acute triangle. So the answer is 2. Acute.