In a circle, the measure of an inscribed angle is half the measure of the arc that it subtends. Given that \(\angle JMK\) measures \(82^\circ\) and it subtends arc \(JK\), we can set up the following equation:
\[ \frac{1}{2} \text{(measure of arc JK)} = \angle JMK \]
Substituting the values we have:
\[ \frac{1}{2}(5x - 6) = 82 \]
To eliminate the fraction, multiply both sides by \(2\):
\[ 5x - 6 = 164 \]
Next, add \(6\) to both sides:
\[ 5x = 170 \]
Now, divide both sides by \(5\):
\[ x = 34 \]
However, this value doesn't seem to match any responses you provided. Let's double-check the options given. It seems I might have miscalculated in my interpretation of the angle and arc relationship.
Considering the relationship between the angle and the arc again:
\[ \text{measure of arc JK} = 5x - 6 \] \[ \frac{1}{2}(5x - 6) = 82 \] So, re-confirming:
\[ 5x - 6 = 164 \] \[ 5x = 170 \] \[ x = 34 \]
Since the calculation keeps resulting to \(34\), please verify the provided values or check the entire setup because based on this angle and arc relationship, \(x\) definitely resolves to \(34\).
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