In Triangle ABC, the side AB is produced to E and side CA is produced to D. If…

When a side of a triangle is produced (extended) beyond a vertex, the exterior angle formed there and the interior angle at that vertex lie on a straight line and form a linear pair, so they are supplementary (sum to 180 degrees). Independently, the three interior angles of any triangle always sum to 180 degrees.

1. Since side CA is produced to D, angle BAD is the exterior angle at vertex A. By the linear pair property, interior angle BAC = 180 degrees minus angle BAD = 180 degrees minus 125 degrees = 55 degrees.

2. Since side AB is produced to E, angle EBC is the exterior angle at vertex B. By the linear pair property, interior angle ABC = 180 degrees minus angle EBC = 180 degrees minus 100 degrees = 80 degrees.

3. By the angle-sum property of a triangle, angle ACB = 180 degrees minus angle BAC minus angle ABC = 180 degrees minus 55 degrees minus 80 degrees = 45 degrees.

4. The difference between angle ABC and angle ACB = 80 degrees minus 45 degrees = 35 degrees.

Cross-check: 55 degrees plus 80 degrees plus 45 degrees = 180 degrees, confirming the angle-sum property holds, so these three interior angles are consistent. Since all three angles are different, the triangle is not isosceles. By the rule that a longer side lies opposite a larger angle, BC (opposite the 55 degree angle) is longer than AB (opposite the 45 degree angle), so AB greater than BC does not hold. Also, the difference between angle BAC (55 degrees) and angle ACB (45 degrees) is 10 degrees, not 20 degrees.

Hence, the statement that holds true is that the difference between angle ABC and angle ACB is 35 degrees.