In circle M , ∠JMK has a measure of 82 degrees and arc JK has a measure of 5x−6 degrees. Find the value of x. (1 point) Responses x is 17.6 units. x is 17.6 units. x is 82 units. x is 82 units. x is 41 units. x is 41 units. x is 14.8 units.

Question

GPT-4o mini · Answer

In a circle, the measure of an inscribed angle is half the measure of the arc that it subtends. Given that $∠ J M K$ measures $82^{\circ}$ and it subtends arc $J K$ , we can set up the following equation:

$\frac{1}{2} (measure of arc JK) = ∠ J M K$

Substituting the values we have:

$\frac{1}{2} (5 x - 6) = 82$

To eliminate the fraction, multiply both sides by $2$ :

$5 x - 6 = 164$

Next, add $6$ to both sides:

$5 x = 170$

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:

$measure of arc JK = 5 x - 6$ $\frac{1}{2} (5 x - 6) = 82$ So, re-confirming:

$5 x - 6 = 164$ $5 x = 170$ $x = 34$

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 $34$ .