Question

in circle n, $overline{kl} cong overline{ml}$. what is the measure of $angle jnk$?
$(13x + 2)^circ$
$(5x + 24)^circ$
$(8x - 3)^circ$
$(7x + 7)^circ$
$66^circ$
$74^circ$
$77^circ$
$80^circ$

Explanation:

Step1: Set arcs equal (congruent chords)

Since $\overline{KL} \cong \overline{ML}$, their corresponding arcs are congruent:
$7x + 7 = 8x - 3$

Step2: Solve for $x$

Rearrange to isolate $x$:
$7 + 3 = 8x - 7x$
$10 = x$

Step3: Find arc $JK$

Substitute $x=10$ into arc $JK$ expression:
$5x + 24 = 5(10) + 24 = 50 + 24 = 74$

Step4: Relate arc to central angle

The measure of central angle $\angle JNK$ equals the measure of its intercepted arc $\overset{\frown}{JK}$.

Answer:

74°