Question

solve for x.
(4x + 54)°
(126 - 2x)°
x =

Explanation:

Step1: Identify angle - relationship

Assume the angles $(4x + 54)^{\circ}$ and $(126-2x)^{\circ}$ are either vertical angles (equal) or supplementary angles (sum to $180^{\circ}$). Since they are corresponding angles formed by a transversal intersecting two parallel lines (indicated by arrow - heads on lines $LM$ and $NO$), they are equal. So we set up the equation $4x + 54=126 - 2x$.

Step2: Add $2x$ to both sides

$4x+2x + 54=126-2x+2x$
$6x + 54=126$

Step3: Subtract 54 from both sides

$6x+54 - 54=126 - 54$
$6x=72$

Step4: Divide both sides by 6

$\frac{6x}{6}=\frac{72}{6}$
$x = 12$

Answer:

$12$