In the given figure, A, B, C, D, and E are points on the circumference of the circle. Line AB is parallel to line DC and line FAG is tangent to the circle at A. Angle GAB = 25^ exto and angle ABC = 10

The sum of opposite angles in a cyclic quadrilateral is $180^\circ$.

$$\angle ADC + \angle ABC = 180^\circ$$

Given $\angle ABC = 100^\circ$:

$$\angle ADC + 100^\circ = 180^\circ$$ $$\angle ADC = 180^\circ - 100^\circ$$ $$\angle ADC = 80^\circ$$

The angle between the tangent FAG and chord AC ($\angle GAC$) is equal to the angle in the alternate segment ($\angle ADC$).

$$\angle GAC = \angle ADC$$ $$\angle GAC = 80^\circ$$

$$\angle GAC = \angle GAB + \angle BAC$$

Given $\angle GAB = 25^\circ$:

$$80^\circ = 25^\circ + \angle BAC$$ $$\angle BAC = 80^\circ - 25^\circ$$ $$\angle BAC = 55^\circ$$

The size of $\angle BAC$ is:

$$\boxed{55^\circ}$$

Since AB is parallel to DC, and AC is a transversal, the alternate interior angles are equal.

$$\angle BAC = \angle ACD$$

From part (a), $\angle BAC = 55^\circ$:

$$\angle ACD = 55^\circ$$

Angles subtended by the same arc at the circumference are equal. Both $\angle AED$ and $\angle ACD$ subtend arc AD.

$$\angle AED = \angle ACD$$ $$\angle AED = 55^\circ$$

The size of $\angle AED$ is:

$$\boxed{55^\circ}$$