Question

in $odot h$, $overline{ik}congoverline{jk}$, $moverparen{ik}=(11x + 2)^{circ}$, and $moverparen{jk}=(12x - 7)^{circ}$. what is the measure of $overparen{ik}$? $moverparen{ik}=square^{circ}$

Explanation:

Step1: Set up the equation

Since $\overline{IK}\cong\overline{JK}$, then $m\widehat{IK}=m\widehat{JK}$. So, $11x + 2=12x - 7$.

Step2: Solve for x

Subtract $11x$ from both sides: $2=x - 7$. Then add 7 to both sides, we get $x = 9$.

Step3: Find the measure of $\widehat{IK}$

Substitute $x = 9$ into the expression for $m\widehat{IK}$, $m\widehat{IK}=11x+2=11\times9 + 2=99 + 2=101$.

Answer:

$101$