Answer: 53°
Explanation: The problem involves the concept of supplementary angles. In a straight line, the sum of angles is 180°. Given that \(\angle PQR\) is 75° and \(\angle PQS\) is 22°, we can find \(\angle SQR\) by subtracting the sum of these two angles from 180°.
Steps:
- Identify the known angles:
- \(\angle PQR = 75^\circ\)
- \(\angle PQS = 22^\circ\)
- Use the supplementary angle theorem:
\[
\angle PQR + \angle PQS + \angle SQR = 180^\circ
\]
- Substitute the known values:
\[
75^\circ + 22^\circ + \angle SQR = 180^\circ
\]
- Calculate \(\angle SQR\):
\[
\angle SQR = 180^\circ - 75^\circ - 22^\circ = 83^\circ
\]
- Correct the calculation:
\[
\angle SQR = 180^\circ - 97^\circ = 83^\circ
\]
The correct calculation should be:
\[
\angle SQR = 180^\circ - 75^\circ - 22^\circ = 83^\circ
\]
Therefore, the measure of \(\angle SQR\) is 83°.