Triangle ABC is a right triangle with the right angle at vertex A. Point D is on the line AC so that the like BD bisects angle B
So line BD divides the triangle ABC into two triangles, ABD and DBC, and the angle at vertex B is the same for both triangles. Let's give that angle a name, X.
We also know that the angle at vertex D in triangle DBC is 100 degrees. This makes the angle at vertex D in triangle ABD 80 degrees because the two angles must add to 180 degrees.
At this point we know two of the angles in triangle ABD add up to 170 degrees, so the third angle, which we called X, is equal to 10 degrees.
Now we know two of the angles in triangle DBC, one is X (= 10 degrees) and the other is 100 degrees. So the angle at vertex C must be 70 degrees.