The quadrilateral ABCD is inscribed in a circle. The ABD angle is 78 °, the CAD angle is 40 °. Find the angle ABC.
| May 5, 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 = 78 * 2 = 156.
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 = 40 * 2 = 800.
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 = 156 + 80 = 236.
Then the angle ABC is equal to half of the degree measure of the arc AC.
Angle ABC = 236/2 = 118.
Answer: Angle ABC is 118.
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