Question

angle psr measures 99°. what is the measure of ∠psq in degrees? (3x + 18)° (9x - 27)° options: 9°, 24°, 45°, 54°

Explanation:

Step1: Set up the angle sum 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 the equation becomes \(12x-9 = 99\).

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 the measure of \(\angle PSQ\)

Substitute \(x = 9\) into the expression for \(\angle PSQ\) which is \(3x + 18\).
\(3\times9+18=27 + 18=45\).

Answer:

\(45^{\circ}\) (corresponding to the option "45°")