Quadrilateral ABCD is inscribed in a circle, angle ABD = 28, angle CAD = 44. Find the angle ABC.

The inscribed angle ABD rests on the arc AD. The inscribed angle ACD rests on the same arc AD, then the degree measures of these angles are the same. Angle ACD = ABD = 28.

In the ACD triangle, we define the value of the ADC angle. Angle ADC = 180 – CAD – ACD = 180 – 44 – 28 = 108.

Since the quadrilateral is inscribed in a circle, the sum of its opposite angles is 180.

Then the angle ABC = 180 – ADC = 180 – 108 = 72.

Answer: Angle ABC is 72.