Question

what is the measure of ∠ink? (4x + 6)° (7x - 21)° 138° 42° x = 9 171°

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle JNM$ and $\angle KNL$ are vertical angles, so $4x + 6=7x - 21$.

Step2: Solve for x

Subtract $4x$ from both sides: $6 = 7x-4x - 21$, which simplifies to $6 = 3x - 21$. Then add 21 to both sides: $6 + 21=3x$, so $27 = 3x$. Divide both sides by 3: $x = 9$.

Step3: Find the measure of $\angle INK$

Substitute $x = 9$ into the expression for $\angle KNL$ (or $\angle JNM$). $\angle KNL=7x - 21$. So $\angle KNL=7\times9 - 21=63 - 21 = 42^{\circ}$.

Answer:

$42^{\circ}$