a = 45o
The reason is the central angle is 90o Any angle drawn from the endpoints of the chord of the 90o angle is 1/2 the central angle.
b is a good deal more complicated.
Draw a line from the circle's center to the tangent point contact. You have just constructed an isosceles triangle.
The central angle is 110 degrees of that isosceles triangle. The other two angles are (180 - 110)/2 = 35 degrees each.
The difference between a and the 35 degree angle is 45 - 35 = 10 degrees.
b + 10 = 90
b = 80
a + b = 80 + 45 = 125