a. The size of the angle x between the chord and the tangent line to the circle at one of the vertex of the triangle is equal to 53° degrees
b. The Alternate segment theorem allows you to find x.
How to evaluate for the angle x between the chord and tangent line.
The angle between a chord and a tangent is equal to the angle in the alternate segment, this is the angle subtended by the chord in the opposite side of the previous angle. This angle is also equal to the measure of the intercepted arc divided by 2.
a. This implies that the angle x is equal to 53°,
b. The theorem which allows you to find x is called the Alternate segment theorem.
Therefore, the measure of the angle x between the chord and the tangent line is 53° because of the Alternate segment theorem.