regularity find the value of x.

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc.

Step2: Identify the intercepted arc

The inscribed angle (x) intercepts arc (RT) which has a measure of (64^{\circ}).

Step3: Calculate the value of (x)

By the inscribed - angle theorem, (x=\frac{1}{2}\times) measure of arc (RT). So (x = \frac{1}{2}\times64^{\circ}). [x = 32^{\circ}]

Answer:

(32^{\circ})