The chords of the circle AB and CD intersect each other. The BAD angle is 40 degrees, the ABD

The chords of the circle AB and CD intersect each other. The BAD angle is 40 degrees, the ABD angle is 30 degrees. Find the corner ADB.

First way.

In the resulting triangle AВD, the value of the angle ADВ = 180 – ВAD – ВD = 180 – 40 – 30 = 110.

Second way.

The inscribed angle of the ADВ is equal to half of the degree measure of the arc of the ACB on which it rests.

Degree measure of the arc AСВ = 360 – AD – ВD.

Degree measure of the arc BP = 2 * 30 = 60.

Degree measure of the arc ВD = 2 * 40 = 80.

Then the arc ACB = 360 – 60 – 80 = 220.

ADВ angle = 220/2 = 110.

Answer: The ADВ angle is 110.