Question

angle psr measures 99°. what is the measure of ∠psq in degrees? 9° 24° 45° 54°

Explanation:

Step1: Set up equation

Since \(\angle PSR=\angle PSQ+\angle QSR\), we have \((3x + 18)+(9x-27)=99\).
Simplify the left - hand side: \(3x+18 + 9x-27=12x-9\).
So, \(12x-9 = 99\).

Step2: Solve for \(x\)

Add \(9\) to both sides of the equation: \(12x-9+9=99 + 9\), which gives \(12x=108\).
Divide both sides by \(12\): \(x=\frac{108}{12}=9\).

Step3: Find \(\angle PSQ\)

Substitute \(x = 9\) into the expression for \(\angle PSQ\) (\(3x + 18\)).
\(\angle PSQ=3\times9+18=27 + 18=45^{\circ}\).

Answer:

\(45^{\circ}\) (the option \(45^{\circ}\))