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 angle relationship

We know that \(\angle PQR=\angle PQS + \angle SQR\).

Step2: Substitute the known values

Given \(\angle PQR = 75^{\circ}\) and \(\angle PQS=22^{\circ}\), then \(\angle SQR=\angle PQR-\angle PQS\).

Step3: Calculate the value of \(\angle SQR\)

\(\angle SQR = 75^{\circ}- 22^{\circ}=53^{\circ}\)

Answer:

\(\angle SQR = 53^{\circ}\), so the correct option is \(53^{\circ}\) (the third option).