Question

$mangle vwx = mangle wvy$ because they are alternate interior angles.$mangle wxv = mangle xvz$ because they are alternate interior angles.$mangle wvy + x^circ + mangle xvz = 180^circ$ because the three angles form a straight line.so the value of $x$ must be 78after moving the vertices, the new value of $x$ is $square^circ$

Explanation:

Step1: Recall triangle angle sum rule

The sum of interior angles of a triangle is $180^\circ$.

Step2: Substitute known angles

$\angle VWX = 56^\circ$, $\angle WXV = x^\circ$, $\angle XVW = 58^\circ$
$56 + x + 58 = 180$

Step3: Calculate the value of x

$x = 180 - 56 - 58$
$x = 66$

Answer:

$66$