Answer: A
Step-by-step explanation: To solve this problem, we need to use the properties of triangles and the given information to determine the measure of angle C.
First, we can use the fact that angle A is opposite angle C to deduce that angles A and C are congruent (i.e. they have the same measure). This means that the measure of angle C is 25 degrees.
Next, we can use the fact that triangle AABC is isosceles (i.e. it has two sides of equal length) to deduce that angle B is also 25 degrees. This is because the sum of the interior angles of a triangle is 180 degrees, so if angle A is 25 degrees and angle C is 25 degrees, then the remaining angle, angle B, must be 180 - (25 + 25) = 130 degrees.
We can also use the fact that triangle AEFG is isosceles to deduce that angle F is also 100 degrees. This is because the sum of the interior angles of a triangle is 180 degrees, so if angle E is 100 degrees, then the remaining angle, angle F, must be 180 - 100 = 80 degrees.
Finally, we can use the given information that the measure of angle Z is 25 degrees and the measure of angle F is 100 degrees to deduce that the measure of angle X is 180 - (25 + 100) = 55 degrees. This is because the sum of the interior angles of a triangle is 180 degrees, and we have already determined the measures of two of the angles (angles Z and F).
Therefore, the measure of angle C is 25 degrees, which means the correct answer is A) 125 degrees.