Given that 𝐵𝐶 is a tangent to the circle, find the measure of angle 𝐴𝐵𝐶 and 𝑦 degrees.
In order to calculate the angle 𝐴𝐵𝐶, we need to use the alternate segment theorem. This states that an angle between a tangent and a cord through the point of contact is equal to the angle in the alternate segment. In our example, this means that angle 𝐴𝐵𝐶 is equal to angle 𝐴𝐷𝐵. This means that angle 𝐴𝐵𝐶 is equal to 113 degrees.
In order to calculate 𝑦, we can use the fact that the inscribed angle, in this case 113 degrees, is half the measure of its intercepted arc. This means that 𝑦 is equal to 113 degrees multiplied by two. 113 multiplied by two is 226. Therefore, 𝑦 is equal to 226 degrees.