In a regular polygon the measure of each angle is (180(n-2))/n, where n is the number of sides (or angles because they are the same). Notice that polygon ABDFH has 5 sides (it's a pentagon), and polygon ABCEGJ has 6 sides (it's a hexagon). Angle ABD is part of the pentagon and angle ABC is part of the hexagon.
∠ABD = (180(5-2))/5 = 180(3)/5 = 108°
∠ABC = (180(6-2))/6 = 180(4)/6 = 120°
∠ABC = ∠ABD + ∠CBD
I'll let you find the measure of angle CBD.