Question

Find the angle ADC.​

Answer 1

To find ∠ADC: Central angle theorem.

Construct a point O so that it is the center of the circle.

Then, ∠AOC=2∠ABC, ∠AOC=80°

Then, ∠AOC=2∠ADC, ∠ADC=40°

So we can find out any angles formed by the points A and C, and D is always equivalent to 40°, regardless of the position of D.

(An example of central angle theorem is in the attachment.)