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Explanation:

Step1: Set up the equation

Since the two angles are vertical angles, they are equal. So, \(3x - 3=6(x - 10)\).

Step2: Expand the right - hand side

Using the distributive property \(a(b + c)=ab+ac\), we have \(3x - 3 = 6x-60\).

Step3: Move the \(x\) terms to one side

Subtract \(3x\) from both sides: \(-3=6x - 3x-60\), which simplifies to \(-3 = 3x-60\).

Step4: Isolate the \(x\) term

Add \(60\) to both sides: \(-3 + 60=3x\), so \(57 = 3x\).

Step5: Solve for \(x\)

Divide both sides by \(3\): \(x=\frac{57}{3}\).

Answer:

\(x = 19\)