Question

find the value of ( x ).

Explanation:

Step1: Recall cyclic quadrilateral property

The sum of opposite angles of a cyclic quadrilateral is $180^\circ$. Let the center of the circle be $O$, and let the angle at the center opposite to $\angle PRS$ be $\angle POS$. First, find the supplementary angle of $134^\circ$:
$180^\circ - 134^\circ = 46^\circ$

Step2: Use tangent-chord angle theorem

The angle between a tangent and a chord is equal to the angle in the alternate segment. For two tangents from an external point, the angle at the external point is half the difference of the measures of the intercepted arcs. The major arc $PRS$ is $134^\circ$, so the minor arc $P R$ is $360^\circ - 134^\circ = 226^\circ$. Then:
$x^\circ = \frac{1}{2} \times (226^\circ - 134^\circ)$

Step3: Calculate the value of $x$

Simplify the expression:
$x^\circ = \frac{1}{2} \times 92^\circ = 46^\circ$

Answer:

$46^\circ$