Question

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Explanation:

Step1: Use the property of parallel lines and angles

Since the line is parallel to one side of the right - angled triangle, by the property of alternate interior angles in a right - angled triangle, we know that \((3x - 1)^{\circ}+31^{\circ}=90^{\circ}\) (because the non - right angles of a right - angled triangle are complementary).

Step2: Solve the equation for \(x\)

First, simplify the equation \(3x-1 + 31=90\).
Combine like terms: \(3x+30 = 90\).
Subtract 30 from both sides: \(3x=90 - 30\), so \(3x=60\).
Divide both sides by 3: \(x=\frac{60}{3}=20\).

Answer:

\(x = 20\)