This diagram represents a circle with an angle of 168° at $\angle XWY$, and you are tasked to solve for $x$, which is the inscribed angle subtended by the same arc $XY$.

Key Concept:

The measure of an inscribed angle is half the measure of the central angle subtended by the same arc. Here, $\angle XWY$ is the central angle subtended by the arc $XY$, and $x$ is the inscribed angle subtended by the same arc.

Formula:

$x = \frac{\text{central angle}}{2}$

Calculation:

$x = \frac{168^\circ}{2} = 84^\circ$

Final Answer:

$x = 84^\circ$

Let me know if you would like further explanation or have any questions!

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Here are some additional related questions for exploration:

1. What is the relationship between a central angle and an inscribed angle?
2. How would the value of $x$ change if $\angle XWY$ was increased to 180°?
3. What happens to $x$ if the central angle becomes obtuse?
4. Can the central angle ever be smaller than the inscribed angle? Why or why not?
5. What would be the arc length corresponding to $\angle XWY$ if the circle's radius was given?

Tip: Always identify the relationship between central and inscribed angles when working with circles!