Question

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

Explanation:

Step1: Set up the equation

Since \(\angle PSR=(3x + 18)+(9x-27)\) and \(\angle PSR = 99^{\circ}\), we have the equation \((3x + 18)+(9x-27)=99\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(3x+9x+18 - 27=99\), which simplifies to \(12x-9 = 99\).

Step3: Solve for \(x\)

Add \(9\) to both sides: \(12x=99 + 9=108\). Then divide both sides by \(12\): \(x=\frac{108}{12}=9\).

Step4: Find the measure of \(\angle PSQ\)

Substitute \(x = 9\) into \(3x + 18\). We get \(3\times9+18=27 + 18=45\).

Answer:

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