The indicated measure is:55⁰
To prove that thry are the circles diameters you can do it by two methods.One is calculating all the angles and the sum of all angles of it equals 360⁰.The one that is the opposite point of 55⁰ is 55⁰ so we need to find the other by : 180⁰-55⁰=125⁰. So 125⁰×2+55⁰×2=360⁰.
The second method is by knowing the rule that applies to diameters of a circle and that says that : a diameter is formed when a line goes from a point to the circle and passes the main point and then finishes to another point in the cirlcle.