Question

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 equation based on angle - addition

Since $\angle PSR=\angle PSQ+\angle QSR$, we have $(3x + 18)+(9x - 27)=99$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms: $(3x+9x)+(18 - 27)=99$, which simplifies to $12x-9 = 99$.

Step3: Solve for $x$

Add 9 to both sides of the equation: $12x-9 + 9=99 + 9$, so $12x=108$. 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 $\angle PSQ$ which is $3x + 18$. So $\angle PSQ=3\times9+18=27 + 18=45$.

Answer:

$45^{\circ}$