Question

in the figure below, $\triangle vwx$ is drawn. the line $yvz$ is drawn such that $yvz \parallel wx$.
$m\angle vwx = m\angle wvy$ because they are alternate interior angles.
$m\angle wxv = m\angle xvz$ because they are alternate interior angles.
$m\angle wvy + x^\circ + m\angle xvz = 180^\circ$ because the three angles form a straight line.
so the value of $x$ must be 78
after moving the vertices, the new value of $x$ is $square^\circ$

Explanation:

Step1: Identify alternate interior angles

Since $YVZ \parallel WX$, $\angle WVY = \angle VWX = 39^\circ$, and $\angle XVZ = \angle WXV = 63^\circ$.

Step2: Use straight angle sum property

The angles $\angle WVY$, $x^\circ$, and $\angle XVZ$ form a straight line, so their sum is $180^\circ$.
$\angle WVY + x + \angle XVZ = 180^\circ$
Substitute values: $39 + x + 63 = 180$

Step3: Solve for x

Combine constants: $102 + x = 180$
Calculate $x$: $x = 180 - 102$

Answer:

78