smc-492640-Vertically opposite

In the diagram below, \(QR\) is parallel to lines \(SU\) and \(VW\).

Find the value of \(x^{\circ}\), giving reasons for your answer. (3 marks)

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\(\angle UTQ = 125^{\circ}\ \ \text{(corresponding angles)} \)

\(\angle STX=125^{\circ}\ \ \text{(vertically opposite angles)}\)

\(x^{\circ} = 180-125=55^{\circ} \ \ \text{(cointerior angles)}\)

Show Worked Solution

\(\angle UTQ = 125^{\circ}\ \ \text{(corresponding angles)} \)

\(\angle STX=125^{\circ}\ \ \text{(vertically opposite angles)}\)

\(x^{\circ} = 180-125=55^{\circ} \ \ \text{(cointerior angles)}\)