In a circle, the measure of an inscribed angle (like ∠JMK) is half the measure of the intercepted arc (arc JK). Therefore, we can set up the equation based on the given information:
\[ \angle JMK = \frac{1}{2} \times \text{arc} JK \]
Given: \[ \angle JMK = 82^\circ \] \[ \text{arc} JK = 5x - 6 \]
Substituting these values into the equation gives us:
\[ 82 = \frac{1}{2}(5x - 6) \]
To eliminate the fraction, multiply both sides by 2:
\[ 164 = 5x - 6 \]
Now, add 6 to both sides:
\[ 164 + 6 = 5x \]
\[ 170 = 5x \]
Next, divide both sides by 5 to solve for \(x\):
\[ x = \frac{170}{5} \]
\[ x = 34 \]
However, it seems this result (34) does not match any given options. Let's verify everything.
Substituting again:
If \(x = 34\), \[ \text{arc} JK = 5(34) - 6 = 170 - 6 = 164 \] And, \[ \angle JMK = \frac{1}{2} \cdot 164 = 82^\circ \]
Since we misinterpreted the original options, the correct computation aligns with \(x = 34\), which isn't in the options provided. Therefore, please ensure that the values provided or the context is correct.
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