# The quadrilateral ABCD is inscribed in a circle. The ABD angle is 71 degrees, the CAD angle is 61 degrees. Find ABC.

October 13, 2021 | education

| The ABD angle is based on the AD arc, the degree measure of which is equal to two values of the ABD angle.

Arc AD = 61 * 2 = 122.

The CAD angle rests on the CD arc, the degree measure of which is equal to two values of the CAD angle.

Arc CD = 71 * 2 = 142.

The angle ABC is based on the arc AC, the degree measure of which is equal to the sum of the arcs AD and CD.

Arc AC = 122 + 142 = 264.

Then the angle ABC is equal to half of the degree measure of the arc AC.

Angle ABC = 264/2 = 44.

Answer: Angle ABC is 132.

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