Question
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.
Answers
GPT-4o mini
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 \(34\).
\[
\frac{1}{2} \text{(measure of arc JK)} = \angle JMK
\]
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 \(34\).