A tangent a and a chord CD are drawn through the point C of the circle, cutting off a smaller arc equal to 80

A tangent a and a chord CD are drawn through the point C of the circle, cutting off a smaller arc equal to 80 degrees. Find the angle between them.

From the center of the circle O draw the radii OS and OD.
The СOD triangle is isosceles, since OС = OD = R.
Since the degree measure of the СD arc, by condition, is 800, the central angle of the СD is also 800.
Then the angle ODС = ODС = (180 – SOD) / 2 = (180 – 80) / 2 = 100/2 = 50.
The radius of the OS is perpendicular to the tangent “a”, since it is drawn to the point of tangency C, then the angle OСA = 90.
Then the angle DСA = OCA – OСD = 90 – 50 = 40.
Answer: The angle between the tangent and the chord is 40.