Question

look at this diagram:
if \\( \overrightarrow { o q } \\) and \\( \overrightarrow { r t } \\) are parallel lines and \\( m \angle r s p = 126 ^ { \circ } \\), what is \\( m \angle q p s \\) ?
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work it out
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Explanation:

Step1: Use the property of adjacent angles

Adjacent angles on a straight line sum to \(180^{\circ}\). Since \(\angle RSP\) and \(\angle QPS\) are adjacent angles formed by the intersection of a transversal with parallel lines \(RT\) and \(OQ\).
Let \(m\angle QPS = x\). We know that \(m\angle RSP+x = 180^{\circ}\) (linear - pair of angles).

Step2: Solve for \(x\)

Given \(m\angle RSP=126^{\circ}\). Substitute into the equation \(126^{\circ}+x = 180^{\circ}\).
Then \(x=180^{\circ}- 126^{\circ}\).

$$x = 54^{\circ}$$

Answer:

\(54\)