inscribed angles\nfind the value of x.\n$x = ? ^{\\circ}$

Explanation:

Step1: Identify the inscribed angle and intercepted arc

The angle $59^{\circ}$ is an inscribed angle that intercepts the arc labeled $x$.

Step2: Apply the Inscribed Angle Theorem

The measure of an inscribed angle is half the measure of its intercepted arc. $$59^{\circ} = \frac{1}{2}x$$

Step3: Solve for $x$

Multiply both sides by 2 to find the arc measure. $$x = 2 \cdot 59^{\circ}$$ $$x = 118^{\circ}$$

Answer:

$x = 118$