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

Explanation:

Step1: Set up an equation

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

Step2: Simplify the left - hand side of the equation

Combine like terms: $3x+9x+18 - 27=12x - 9$. So the equation becomes $12x-9 = 99$.

Step3: Solve for x

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

Step4: Find the measure of $\angle PSQ$

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

Answer:

$45^{\circ}$