Question

in the figure below, $\triangle vwx$ is drawn. the line $overleftrightarrow{yvz}$ is drawn such that $overleftrightarrow{yvz} parallel overline{wx}$.$mangle vwx = mangle wvy$ because they are alternate interior angles$mangle wxv = mangle xvz$ because they are alternate interior angles$mangle wvy + x + mangle xvz = 180^circ$ because the three angles form a straight lineso the value of $x$ must be

Explanation:

Step1: Identify alternate interior angles

From parallel lines $\overleftrightarrow{YVZ} \parallel \overleftrightarrow{WX}$, we get:
$m\angle VWX = m\angle WVY = 57^\circ$, $m\angle WXV = m\angle XVZ = 45^\circ$

Step2: Use straight line angle sum

The angles on line $\overleftrightarrow{YVZ}$ sum to $180^\circ$:
$m\angle WVY + x + m\angle XVZ = 180^\circ$
Substitute values: $57 + x + 45 = 180$

Step3: Solve for $x$

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

Answer:

$78^\circ$