Question

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

Explanation:

Step1: Use the property of congruent chords

Since $KL\cong ML$, the central - angles subtended by these chords are equal. Let's first find the value of $x$ using the fact that the sum of the central - angles of a circle is $360^{\circ}$.
The central - angles in the circle are $(5x + 24)^{\circ}$, $(13x+2)^{\circ}$, $(8x - 3)^{\circ}$, and $(7x + 7)^{\circ}$.
So, $(5x + 24)+(13x+2)+(8x - 3)+(7x + 7)=360$.
Combining like - terms: $(5x+13x + 8x+7x)+(24 + 2-3 + 7)=360$.
$33x+30 = 360$.

Step2: Solve for $x$

Subtract 30 from both sides of the equation: $33x=360 - 30=330$.
Divide both sides by 33: $x=\frac{330}{33}=10$.

Step3: Find the measure of $\angle JNK$

The measure of $\angle JNK=(5x + 24)^{\circ}$.
Substitute $x = 10$ into the expression: $5\times10+24=50 + 24=74^{\circ}$.

Answer:

$74^{\circ}$