what are the angle properties of a circle?

The radius of  a circle meets the tangent of the circle at
right angles at the tangent point.

The chord of a circle
subtends an angle which is twice that of the angle it makes on the
circumference.

The angles a chord makes on the same side of
the circumference are equal,

The sum of the diagonally
opposite angles of a concylic quadrilateral  is equal to 180
degrees.

The sum of all the exterior angles of a concyclic
polygon  is 360 degrees.