Question

the measure of ∠kjn is 92°. what is the measure of ⌢jmk?

Explanation:

Step1: Recall the tangent - chord theorem

The measure of the angle formed by a tangent and a chord is half the measure of the intercepted arc. Here, $\angle KJN$ is the angle formed by the tangent $ON$ and the chord $JK$, and the intercepted arc is $\overparen{JMK}$.

Step2: Set up the equation

Let the measure of $\overparen{JMK}$ be $x$. According to the theorem, $\angle KJN=\frac{1}{2}\text{measure of }\overparen{JMK}$. We know that $\angle KJN = 92^{\circ}$. So, $92^{\circ}=\frac{1}{2}x$.

Step3: Solve for $x$

Multiply both sides of the equation $92^{\circ}=\frac{1}{2}x$ by 2. We get $x = 184^{\circ}$.

Answer:

$184^{\circ}$