Question

question 9 of 10 what is the measure of arc jl? a. 96° b. 168° c. 42° d. 84°

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. Here, the inscribed angle $\angle{JLK}=84^{\circ}$, and it intercepts arc $\overset{\frown}{JK}$. Let the measure of arc $\overset{\frown}{JK}$ be $x$. Then $\angle{JLK}=\frac{1}{2}x$.

Step2: Solve for the measure of arc $\overset{\frown}{JK}$

Since $\angle{JLK} = 84^{\circ}$ and $\angle{JLK}=\frac{1}{2}x$, we have $84^{\circ}=\frac{1}{2}x$. Solving for $x$, we get $x = 168^{\circ}$. So the measure of arc $\overset{\frown}{JK}$ is $168^{\circ}$.

Answer:

B. 168°