The quadrilateral ABCD is inscribed in a circle. The ABC angle is 138 °, the CAD angle is 83 °.
| February 23, 2021 | education
The quadrilateral ABCD is inscribed in a circle. The ABC angle is 138 °, the CAD angle is 83 °. Find the ABD angle. give the answer in degrees.
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 = 83 * 2 = 166.
The angle ABC is based on the arc AC, the degree measure of which is equal to two values of the angle ABC.
Arc AC = 2 * 138 = 276.
The arc AC is also equal to the sum of the degree measures of the arcs AD and CD.
276 = AD + 166.
Arc AD = 276 – 166 = 110.
Then the angle ABD = 110/2 = 55.
Answer: Angle ABD is 55.
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