Question

if \\( \angle pqr \\) measures \\( 75 ^ { \circ } \\), what is the measure of \\( \angle \\) sqr? \\( 22 ^ { \circ } \\) \\( 45 ^ { \circ } \\) \\( 53 ^ { \circ } \\) \\( 97 ^ { \circ } \\)

Explanation:

Step1: Analyze the relationship between angles

We know that \(\angle PQR=\angle PQS+\angle SQR\). Given \(\angle PQR = 75^{\circ}\) and \(\angle PQS=22^{\circ}\)

Step2: Solve for \(\angle SQR\)

Using the formula \(\angle SQR=\angle PQR - \angle PQS\), substitute the values: \(\angle SQR=75^{\circ}- 22^{\circ}\)

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Answer:

\(53^{\circ}\) (the third option)