Question

segment $qn$ bisects angle $pqs$ such that the measure of angle $pqn=(12x + 4)^{circ}$, and the measure of angle $nqs=(18x - 14)^{circ}$. find the value of $x$.

Explanation:

Step1: Recall angle - bisector property

Since $QN$ bisects $\angle PQS$, then $\angle PQN=\angle NQS$.
So, we set up the equation $12x + 4=18x-14$.

Step2: Isolate the variable terms

Subtract $12x$ from both sides of the equation:
$12x + 4-12x=18x-14 - 12x$
$4 = 6x-14$.

Step3: Isolate the $x$ - term further

Add 14 to both sides of the equation:
$4 + 14=6x-14 + 14$
$18 = 6x$.

Step4: Solve for $x$

Divide both sides by 6:
$\frac{18}{6}=\frac{6x}{6}$
$x = 3$.

Answer:

$3$