The measures of the angles of def are in the ratio 2: 4: 4. what are the measures of the angles?

So you can simplify that ratio to 1:2:2
DEF is a triangle (there are 3 vertices and therefore 3 sides).
The measures in a triangle add up to 180 degrees.
So you need 2 angles that are twice 1 angle, so set up an equation.

x + 2x + 2x = 180
5x = 180
x = 36
36 is the measure of the smallest angle, so the two other angles are twice that, which are 72 and 72.

So your angles are 36, 72, 72