Question

in ⊙h, (widehat{ik} cong widehat{jk}), (mwidehat{ik} = (11x + 2)^circ), and (mwidehat{jk} = (12x - 7)^circ). what is the measure of (widehat{jk})? (mwidehat{jk} = square^circ)

Explanation:

Step1: Set arc measures equal

Since \(\widehat{IK} \cong \widehat{JK}\), their measures are equal. So, \(11x + 2 = 12x - 7\).

Step2: Solve for \(x\)

Subtract \(11x\) from both sides: \(2 = x - 7\). Then add 7 to both sides: \(x = 9\).

Step3: Find \(m\widehat{JK}\)

Substitute \(x = 9\) into \(12x - 7\): \(12(9) - 7 = 108 - 7 = 101\).

Answer:

\(101\)