Final answer:
To find ∠ABC, subtract the measures of ∠ABD and ∠CBD from 180°.
Step-by-step explanation:
To find the measure of angle ABC, we need to use the fact that BD bisects angle ABD. This means that angles ABD and CBD are congruent, as they are split equally by line BD. Since angle ABD measures 51°, angle CBD also measures 51°. Now we can find angle ABC by subtracting the measures of angles ABD and CBD from 180° (the sum of angles in a triangle).
180° - 51° - 51° = 78°.
Therefore, the measure of angle ABC is 78°.