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

From the figure, 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 \(\angle SQR\)

Substitute the values into the formula: \(\angle SQR = 75^{\circ}-22^{\circ}=53^{\circ}\)

Answer:

\(53^{\circ}\) (corresponding to the third option in the multiple - choice list)