Question

angle psr measures $99^\circ$.
what is the measure of $\angle psq$ in degrees?
$9^\circ$
$24^\circ$
$45^\circ$
$54^\circ$
$\angle psq=(3x + 18)^\circ$, $\angle qsr=(9x - 27)^\circ$

Explanation:

Step1: Set up angle sum equation

$\angle PSQ + \angle QSR = \angle PSR$
$(3x + 18) + (9x - 27) = 99$

Step2: Simplify and solve for $x$

Combine like terms: $12x - 9 = 99$
Add 9 to both sides: $12x = 108$
Divide by 12: $x = \frac{108}{12} = 9$

Step3: Calculate $\angle PSQ$

Substitute $x=9$ into $3x+18$:
$3(9) + 18 = 27 + 18$

Answer:

$45^\circ$ (Option C)