The quadrilateral ABCD is inscribed in a circle. The ABC angle is 110 °, the ABD angle is 70 °. Find the CAD corner.

First way.
The sought inscribed corner of the СAD rests on the arc of the СD.
The inscribed angle of the СВD is based on the same arc of the СD, the value of which is equal to the difference in the angles ABC and AED.
Angle СDВ = ABC – AВD = 110 – 70 = 400.
Then the angle СAD = 400.

Second way.
Since the quadrangle is inscribed in a circle, the sum of its opposite angles is 1800, then the angle ADС = 180 – ABC = 180 – 110 = 700.
In the AСD triangle, the AСD angle is equal to the AED angle and is equal to 700, since they are based on one AD arc.
Then the angle СAD = 180 – ADS – AСD = 180 – 70 – 70 = 400.
Answer: The СAD angle is 400.