Question

find the value of x.

Explanation:

Step1: Set up equation

Since the sum of the two non - overlapping angles \((2x - 5)^{\circ}\) and \(31^{\circ}\) equals the larger angle \(74^{\circ}\), we have the equation \(2x-5 + 31=74\).

Step2: Simplify left - hand side

Combine like terms: \(2x+( - 5 + 31)=74\), so \(2x + 26=74\).

Step3: Isolate the term with \(x\)

Subtract 26 from both sides: \(2x+26 - 26=74 - 26\), which gives \(2x = 48\).

Step4: Solve for \(x\)

Divide both sides by 2: \(\frac{2x}{2}=\frac{48}{2}\), so \(x = 24\).

Answer:

24