Question

in circle n, \\(\overline{kl} \cong \overline{ml}\\). what is the measure of \\(\angle jnk\\)? \\(\bigcirc\\) \\(66^\circ\\) \\(\bigcirc\\) \\(74^\circ\\) \\(\bigcirc\\) \\(77^\circ\\) \\(\bigcirc\\) \\(80^\circ\\)

Explanation:

Step1: Set congruent arcs equal

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

Step2: Solve for x

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

Step3: Find arc JK measure

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

Step4: Relate central angle to arc

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

Answer:

74° (Option B. 74°)