Final answer:
To find the value of x, set the measure of the central angle ∠JLM equal to the expression for the arc measure, then solve for x. After calculation, x is found to be 11.6 when rounded to the nearest tenth.
Step-by-step explanation:
To solve for x when given that ∠JLM=68° and m JM ⌓ = (10x−48)° in circle K, we need to use the property that the measure of an arc's central angle is equal to the measure of the arc itself in degrees. Since ∠JLM is the central angle for arc JM⌓, we can set up the following equation:
68° = (10x − 48)°
Now, we solve for x:
68 = 10x − 48
Add 48 to both sides:
68 + 48 = 10x
116 = 10x
Divide both sides by 10:
x = 11.6
Thus, x is 11.6, rounded to the nearest tenth as necessary.