Question

problem 14: a horizontal line intersected by a transversal, forming a 142° angle and a (-2x + 54)° angle (diagram included).

Explanation:

Step1: Identify supplementary angles

The two angles \(142^\circ\) and \((-2x + 54)^\circ\) are supplementary (they form a linear pair), so their sum is \(180^\circ\).
\[142 + (-2x + 54) = 180\]

Step2: Simplify the equation

Combine like terms:
\[142 + 54 - 2x = 180\]
\[196 - 2x = 180\]

Step3: Solve for \(x\)

Subtract 196 from both sides:
\[-2x = 180 - 196\]
\[-2x = -16\]
Divide both sides by -2:
\[x = \frac{-16}{-2}\]
\[x = 8\]

Answer:

\(x = 8\)