In a circle, the measure of the angle formed by two chords (like ∠JMK) that intercept an arc is half the measure of the arc. We can set up the equation based on the given information:
\[ \frac{1}{2} \cdot \text{arc } JK = \angle JMK \]
Using the measures provided:
\[ \frac{1}{2}(5x - 6) = 82 \]
To eliminate the fraction, multiply both sides by 2:
\[ 5x - 6 = 164 \]
Now, add 6 to both sides:
\[ 5x = 170 \]
Next, divide both sides by 5:
\[ x = 34 \]
Since 34 is not among the options listed, I will reassess the equation setup.
Given the angle measure of \( \angle JMK = 82 \):
- Substitute the arc measurement into the circle angle formula: \[ \angle JMK = \frac{1}{2} \cdot \text{arc } JK \]
- Using \( \text{arc } JK \) as \( 5x - 6 \): \[ 82 = \frac{1}{2}(5x - 6) \]
Multiply through by 2: \[ 164 = 5x - 6 \]
Now add 6 to both sides: \[ 170 = 5x \]
Lastly, divide by 5: \[ x = 34 \]
Since the correct value is still undefined in the offered choices, it suggests a revision of the specifics or options is required. However, the calculations are accurate based on the input provided. If the right answer of \(34\) is not present, please reconfirm the given options or parameters of the circle.
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