Question

find the value of $x$.
$x =$

Explanation:

Step1: Use the property of complementary angles

Since the two angles \(54^{\circ}\) and \((3x + 36)^{\circ}\) are complementary (they form a right - angle relationship as the lines are parallel and the transversal creates angles that sum to \(90^{\circ}\)), we have the equation \(54+(3x + 36)=90\).

Step2: Simplify the left - hand side of the equation

First, simplify \(54+(3x + 36)\):

$$
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$$

So the equation becomes \(3x+90 = 90\).

Step3: Solve for \(x\)

Subtract \(90\) from both sides of the equation \(3x+90 = 90\):

$$
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$$

Divide both sides by \(3\): \(x=\frac{0}{3}=0\).

Answer:

\(0\)