Question

1. 4x 5x - 27

Explanation:

Step1: Set up the equation

Since \(4x\) and \(5x - 27\) are supplementary angles (they form a linear - pair and their sum is \(180^{\circ}\)), we have the equation \(4x+(5x - 27)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(4x+5x-27 = 180\), which simplifies to \(9x-27 = 180\).

Step3: Isolate the variable term

Add \(27\) to both sides of the equation: \(9x-27 + 27=180 + 27\), so \(9x=207\).

Step4: Solve for \(x\)

Divide both sides by \(9\): \(x=\frac{207}{9}=23\).

Answer:

\(x = 23\)