Question

if ∠pqr measures 75°, what is the measure of ∠ sqr?
○ 22°
○ 45°
○ 53°
○ 97°

Explanation:

Step1: Identify angle relationship

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

Answer:

\( 53^{\circ} \) (corresponding to the option with \( 53^{\circ} \))