Question

in $odot h$, $overset{\frown}{ik}congoverset{\frown}{jk}$, $moverset{\frown}{ik}=(11x + 2)^{circ}$, and $moverset{\frown}{jk}=(12x - 7)^{circ}$. what is the measure of $overset{\frown}{ikj}$? $moverset{\frown}{ikj}=square^{circ}$

Explanation:

Step1: Set up the equation

Since $\overset{\frown}{IK}\cong\overset{\frown}{JK}$, we have $m\overset{\frown}{IK}=m\overset{\frown}{JK}$. 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 $\overset{\frown}{IK}$ and $\overset{\frown}{JK}$

Substitute $x = 9$ into the expression for $m\overset{\frown}{IK}$ (we could also use the expression for $m\overset{\frown}{JK}$). $m\overset{\frown}{IK}=11x + 2=11\times9+2=99 + 2=101^{\circ}$. And $m\overset{\frown}{JK}=12x-7=12\times9-7=108 - 7 = 101^{\circ}$.

Step4: Find the measure of $\overset{\frown}{IKJ}$

$m\overset{\frown}{IKJ}=m\overset{\frown}{IK}+m\overset{\frown}{JK}=101^{\circ}+101^{\circ}=202^{\circ}$

Answer:

$202$