To solve for \( x \) using the Inscribed Angles Theorem, we must first understand how the angle and arc measurements are related in a circle.
In a circle, the measure of an inscribed angle is half the measure of the intercepted arc. Here, angle \( JMK \) is an inscribed angle that intercepts arc \( JK \).
The formula we will use is: \[ \text{Measure of Angle JMK} = \frac{1}{2} \times \text{Measure of Arc JK} \]
Given:
- Measure of angle \( JMK = 82^\circ \)
- Measure of arc \( JK = 5x - 6 \)
Plugging the given values into the equation: \[ 82 = \frac{1}{2}(5x - 6) \]
Now, multiply both sides of the equation by 2 to eliminate the fraction: \[ 164 = 5x - 6 \]
Next, add 6 to both sides: \[ 164 + 6 = 5x \] \[ 170 = 5x \]
Now, divide both sides by 5: \[ x = \frac{170}{5} = 34 \]
Since \( 34 \) is not one of your provided answer choices, let’s check the choices again carefully.
Looks like we made a mistake in interpretation of choices. Please clarify so if any of those choices is potentially wrong, or if you've double-checked.
\(\text{The correct value based on calculations is } x = 34. \)
1 answer