Question

what is the value of x?

x = \boxed{\circ}

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Explanation:

Step1: Identify right triangle property

Since $WV$ is the diameter of the circle, $\angle WUV = 90^\circ$ (angle inscribed in a semicircle is a right angle).

Step2: Sum angles in triangle

The sum of angles in $\triangle WUV$ is $180^\circ$. So:
$$6x + 60^\circ + 90^\circ = 180^\circ$$

Step3: Simplify and solve for x

Combine constants first:
$$6x + 150^\circ = 180^\circ$$
Subtract $150^\circ$ from both sides:
$$6x = 180^\circ - 150^\circ = 30^\circ$$
Divide by 6:
$$x = \frac{30^\circ}{6} = 5^\circ$$

Answer:

$x = 5$