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Step1: Use the property of adjacent angles on a straight line
Adjacent angles on a straight line sum to \(180^{\circ}\). So, \(121^{\circ}+x^{\circ}=180^{\circ}\)
Step2: Solve for \(x\)
Subtract \(121^{\circ}\) from both sides of the equation: \(x = 180 - 121\)
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\(x = 59\)