what is the value of x? x = ?°

Explanation:

Step1: Recall circle - tangent angle property

The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc. Let the central angle corresponding to the intercepted arc be $y$. The angle between the tangent and the chord is $36^{\circ}$, so the central angle $y = 2\times36^{\circ}=72^{\circ}$.

Step2: Use the inscribed - angle property

The measure of an inscribed angle is half the measure of the central angle subtended by the same arc. The inscribed angle $x$ and the central angle $y$ subtend the same arc. So $x=\frac{y}{2}$. Since $y = 72^{\circ}$, then $x = 36^{\circ}$.

Answer:

$36$