Question

using the angle formed by a tangent and chord theorem
the measure of ∠kjn is 92°. what is the measure of \\(\overarc{jmk}\\)?

Explanation:

Step1: Recall the Angle - Tangent and Chord Theorem

The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc. Let the measure of arc \(JMK\) be \(x\). The angle \(\angle KJN = 92^{\circ}\). The formula is \(\angle KJN=\frac{1}{2}\text{measure of arc }JMK\) (since the angle between a tangent \(NO\) and chord \(JK\) intercepts arc \(JMK\)).

Step2: Solve for the measure of arc \(JMK\)

From the formula \(\angle KJN=\frac{1}{2}\text{measure of arc }JMK\), we can rewrite it to find the measure of arc \(JMK\). Multiply both sides of the equation \(92^{\circ}=\frac{1}{2}x\) by \(2\). So, \(x = 2\times92^{\circ}\).

Answer:

\(184^{\circ}\)