The quadrilateral ABCD is inscribed in a circle. The ABC angle is 116 degrees, the ABD angle
| September 19, 2021 | education
The quadrilateral ABCD is inscribed in a circle. The ABC angle is 116 degrees, the ABD angle is 37 degrees. Find the CAD angle.
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 = 37 * 2 = 74.
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 * 116 = 232.
The arc AC is also equal to the sum of the degree measures of the arcs AD and CD.
232 = DC + 74.
Arc DC = 232 – 74 = 158.
Then the angle CAD = 158/2 = 79.
Answer: The CAD angle is 79.
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