# The quadrilateral ABCD is inscribed in a circle. Angle ABD = 14 °, angle CAD = 30 °. Find the angle ABC.

June 26, 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 = 14 * 2 = 28.

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

Arc CD = 30 * 2 = 60.

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 = 28 + 60 = 88

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

Angle ABC = 88/2 = 440.

Answer: Angle ABC is 44.

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