1.) Angle DEF is from an equilateral triangle. Since all sides are the same, then all angles are the same, and the angles of a triangle add up to 180º. So 180º/3 = 60º. So, Angle DEF = 60º.
2.) Angles ADE and AED are the same because of that triangle being isosceles. So we can find ADE easier by using the fact that line CDF is one large angle of 180º. All angles in square ABCD are 90º. And, we already know angle EDF is 60º because of it belonging to the equilateral triangle. So to get the value of angle ADE we consider the value of the angle of the line, 180º, then subtract the 90º from the square, and subtract the 60º from the equilateral triangle. 180º-90º-60º=30º. So, angle ADE is 30º.
Since angle ADE = angle AED, AED=30º.
3.) Angle AEF = AED + DEF = 30º + 60º = 90º.
Hence, the size of angle AEF is 90º.