In the figure, BA = AD = DC and point D is on segment BC. The measure of angle ACD is 24 degrees. What is the measure of angle ABC?
Since triangle ADC is an isosceles triangle, then angle DAC = angle ACD = 24 degrees. Thus, angle ADB = angle ACD + angle DAC by exterior angle theorem, so angle ADB = 24 + 24 = 48 degrees. Since triangle ABD is an isosceles triangle, then angle ABD = angle ADB = 48 degrees.
Angle ABC = angle ABD.
Angle ABC = 48 degrees.