Quadrilateral ABCD is inscribed in a circle. The ABC angle is 130 degrees, the CAD angle is 79 degrees.

Quadrilateral ABCD is inscribed in a circle. The ABC angle is 130 degrees, the CAD angle is 79 degrees. Find the angle ABC.

The sum of the opposite angles of the quadrangle inscribed in the circle is 180, then the angle ADC = (180 – ABC) = (180 – 130) = 50.

The sum of the inner angles of the triangle is 180, then in the triangle ACD, the angle ACD = (180 – CAD – ADC) = (180 – 79 – 50) = 51.

The inscribed angle ACD rests on the arc AD. The sought angle ABD rests on the same arc, therefore, the angle ABD = ACD = 51.

Answer: Angle ABD is 51.