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

July 29, 2021 | education

| **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.

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