The 2 red lines on the triangle mean that the 2 sides are equal.
Because the 2 sides are equal, Angle D is the same as angle C.
So now angle C & D are both 52 degrees, we can find Angle E
180 - 52 - 52 = 76 degrees
Angle DEF + Angle E need to equal 180 degrees
Angle DEF = 180 - 76 = 104 degrees