In right triangle $PSQ$, angle $PSR$ measures $99°$. What is the measure of angle $PSQ$ in degrees?

• A. $54°$
• B. $24°$
• C. $45°$
• D. $9°$

Answer: (D)

Verified step by step guidance

1. Identify the triangle involved and the angles given. We have a right triangle \( \triangle PSQ \) and an angle \( \angle PSR \) measuring \( 99^\circ \).
2. Recall that the sum of angles around a point is \( 360^\circ \). Since \( \angle PSR \) and \( \angle PSQ \) share vertex \( S \), consider how these angles relate to each other and the right angle in \( \triangle PSQ \).
3. Note that \( \triangle PSQ \) is a right triangle, so one of its angles is \( 90^\circ \). The sum of the other two angles in the triangle must be \( 90^\circ \) because the total sum of angles in any triangle is \( 180^\circ \).
4. Use the fact that \( \angle PSR \) and \( \angle PSQ \) are supplementary or complementary based on their geometric arrangement. Set up an equation relating \( \angle PSQ \) to \( \angle PSR \) and the right angle.
5. Solve the equation for \( \angle PSQ \) by subtracting the known angles from \( 180^\circ \) or \( 90^\circ \), depending on the relationship established, to find the measure of \( \angle PSQ \).