Question

note that vertical angles are congruent and are thus equal in measure. use this fact to find the value of x.

Explanation:

Step1: Use vertical - angle property

Since vertical angles are congruent, we set up the equation $4x=(90 - x)$.

Step2: Solve the equation for x

Add $x$ to both sides: $4x+x = 90$, which simplifies to $5x=90$.

Step3: Isolate x

Divide both sides by 5: $x=\frac{90}{5}=18$.

Answer:

$x = 18$