Final answer:
Angle ACB is found by using the properties of triangles and the given angles. After determining angles in the isosceles triangle BDC, we can calculate that angle ACB is 75°.
Step-by-step explanation:
To find the value of angle ACB, we must consider the properties of triangles.
Given angle ABC = 45° and angle ADC = 60°, and with the information that DC = 2BD, we can infer that triangle BDC is an isosceles triangle.
Because the angles of a triangle must sum to 180°, angle BDC can be found by subtracting the 60° angle of ADC from 180°, leaving 120° to be split between angle BDC and angle BCD, which are equal due to the isosceles triangle property.
Therefore, angle BDC and angle BCD are both 60°.
Now, considering triangle BCD as part of triangle ABC, we can deduce the measure of angle ACB. Since angle ABC is given as 45°, to find angle ACB, we subtract the 45° of angle ABC and the 60° of angle BCD from the total 180° of triangle ABC, giving us angle angle ACB = 180° - 45° - 60° = 75°.