Question

using the angle formed by a tangent and chord theorem. the measure of ∠kin is 92°. what is the measure of arc jmk?

Explanation:

Step1: Recall the tangent - chord theorem

The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc. Let $\angle KJN = 92^{\circ}$, and the intercepted arc is $\overset{\frown}{JMK}$.

Step2: Apply the formula

According to the theorem, $\angle KJN=\frac{1}{2}\text{measure of }\overset{\frown}{JMK}$. So, $\text{measure of }\overset{\frown}{JMK}=2\times\angle KJN$.

Step3: Calculate the arc measure

Substitute $\angle KJN = 92^{\circ}$ into the formula: $\text{measure of }\overset{\frown}{JMK}=2\times92^{\circ}=184^{\circ}$.

Answer:

$184$