Question

look at this diagram:
diagram of lines oq, rt (parallel) and transversal un, with points o, p, q on oq; r, s, t on rt; u, s, p, n on un. angles: m∠ops = 47°
if \\(\overleftrightarrow{oq}\\) and \\(\overleftrightarrow{rt}\\) are parallel lines and \\(m\angle ops = 47^\circ\\), what is \\(m\angle tsp\\)?
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Explanation:

Step1: Identify alternate interior angles

Since $\overleftrightarrow{OQ} \parallel \overleftrightarrow{RT}$, $\angle OPS$ and $\angle TSP$ are alternate interior angles.

Step2: Apply alternate interior angles theorem

Alternate interior angles of parallel lines are congruent, so $m\angle TSP = m\angle OPS$.
<Expression>$m\angle TSP = 47^\circ$</Expression>

Answer:

$47^\circ$