Question

find the value of x.

what is the measure of the angle that is labeled (3x + 36)?

Explanation:

Step1: Use property of parallel lines and transversal

When two parallel lines are cut by a transversal, the sum of an angle and its corresponding angle (or in this case, using the property that \(54^{\circ}\) and \((3x + 36)^{\circ}\) are supplementary if we consider the linear - pair - like relationship due to parallel lines). So, \(54+(3x + 36)=180\).

Step2: Simplify the equation

First, combine like terms: \(3x+(54 + 36)=180\), which gives \(3x+90 = 180\).
Then, subtract 90 from both sides: \(3x=180 - 90\), so \(3x=90\).

Step3: Solve for \(x\)

Divide both sides by 3: \(x=\frac{90}{3}=30\).

Step4: Find the measure of \((3x + 36)^{\circ}\)

Substitute \(x = 30\) into \(3x+36\). We get \(3\times30+36\).
First, calculate \(3\times30 = 90\), then \(90+36=126\).

Answer:

\(126\)