Question

in circle n, kl ≅ ml. what is the measure of ∠jnk? (13x + 2)° (5x + 24)° (8x - 3)° (7x + 7)° 66° 74° 77° 80°

Explanation:

Step1: Use the property of congruent chords

Since $\overline{KL}\cong\overline{ML}$, the arcs they intercept are congruent. So, $m\overset{\frown}{KL}=m\overset{\frown}{ML}$. That is, $7x + 7=8x - 3$.
Solve for $x$:
$8x-7x=7 + 3$
$x = 10$.

Step2: Find the measure of arc $\overset{\frown}{JK}$

Substitute $x = 10$ into the measure of arc $\overset{\frown}{JK}$. $m\overset{\frown}{JK}=5x+24$.
$m\overset{\frown}{JK}=5\times10 + 24=50+24 = 74^{\circ}$.

Step3: Recall the central - angle theorem

The measure of a central angle is equal to the measure of the arc it intercepts. $\angle JNK$ is a central angle that intercepts arc $\overset{\frown}{JK}$.
So, $m\angle JNK=m\overset{\frown}{JK}$.

Answer:

$74^{\circ}$