Parallel Lines Analysis: Solving the 3α=x Angle Relationship

If the lines are parallel, the two angles will be equal to each other, since alternate angles between parallel lines are equal to each other.

We will check if the angles are equal by substituting the value of X:

$x+\alpha+31=3\alpha+\alpha+31=4\alpha+31$

Now we will compare the angles:

$4\alpha+31=4\alpha+29$

We will reduce on both sides to$4\alpha$We obtain:
$31=29$

Since this theorem is not true, the angles are not equal and, therefore, the lines are not parallel.