Question

solve for the given variable.

x = ____

Explanation:

Step1: Recall the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, for a triangle with angles \(x^{\circ}\), \(114^{\circ}\), and \(31^{\circ}\), we have the equation \(x + 114+31=180\).

Step2: Simplify the left - hand side of the equation

First, add \(114\) and \(31\): \(114 + 31=145\). So the equation becomes \(x+145 = 180\).

Step3: Solve for \(x\)

Subtract \(145\) from both sides of the equation. Using the property \(a + b=c\Rightarrow a=c - b\), we get \(x=180-145\).

Step4: Calculate the value of \(x\)

\(180-145 = 35\).

Answer:

\(35\)