The quadrilateral ABCD is inscribed in a circle. The ABC angle is 48, the CAD angle is 38. Find the ABD angle.

| February 11, 2021 | education

First way.

The degree measure of the AВD angle is equal to half of the degree measure of the blood pressure arc on which this angle rests.

The degree measure of the ABP arc is equal to the difference between the degree measures of the ADС and DС arcs.

The ADС arc is equal to two degree measures of the AВD angle. Arc ADС = 48 * 2 = 96.

The arc of the DС is equal to two degree measures of the СBP angle. Arc DС = 38 * 2 = 76.

Then the arc of BP = ADС- HP = 96 – 76 = 20.

Then the value of the AВD angle = 20/2 = 10.

Second way.

In an inscribed quadrilateral in a circle, the sum of opposite angles is 1800, then the angle ADС = 180 – 48 = 1320. In the ADС triangle, the angle ADС = 180 – 132 – 38 = 10.

Since the angle of AСD and AВD are based on one arc of the ABP, then the angle of AСD = AВD = 10.

Answer: Angle AВD = 10.



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