Question

find the measure of \\( \angle q t n \\).

\\( m \angle q t n = \square ^ { \circ } \\)

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Explanation:

Step1: Use the property of corresponding angles

Since \(OP\parallel QR\), \(\angle QTN\) and \(\angle OSM\) are corresponding angles. Also, \(\angle OSM\) and \((2x + 55)^{\circ}\) are vertical angles, so \(\angle OSM=(2x + 55)^{\circ}\). And \(\angle QTN=(7x + 25)^{\circ}\). Because \(OP\parallel QR\), \(2x+55 = 7x + 25\).

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Step2: Calculate the measure of \(\angle QTN\)

Substitute \(x = 6\) into \(\angle QTN=(7x + 25)^{\circ}\)

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Answer:

\(67\)