Question

find the measure of ∠pvs. m∠pvs = ( )°

Explanation:

Step1: Note vertical - angle relationship

Vertical angles are equal. So, $143 - 8x=11x - 12$.

Step2: Solve the equation for x

Add $8x$ to both sides: $143=11x - 12+8x$, which simplifies to $143 = 19x-12$. Then add 12 to both sides: $143 + 12=19x$, so $155 = 19x$. Then $x=\frac{155}{19}$.

Step3: Find the measure of $\angle PVS$

Substitute $x$ into the expression for $\angle PVS$ (we can use either $143 - 8x$ or $11x - 12$). Let's use $143 - 8x$.
$143-8\times\frac{155}{19}=\frac{143\times19-8\times155}{19}=\frac{2717 - 1240}{19}=\frac{1477}{19}=77.74$ (approx). But if we assume the lines are parallel and these are corresponding - like angles in a proper geometric setup and we made a wrong start above, and assume they are supplementary.
$143 - 8x+11x - 12 = 180$ (since they are supplementary angles).
Combining like - terms: $131 + 3x=180$.
Subtract 131 from both sides: $3x=180 - 131 = 49$.
$x=\frac{49}{3}$.
Substitute $x$ into $143 - 8x$:
$143-8\times\frac{49}{3}=\frac{143\times3-8\times49}{3}=\frac{429-392}{3}=\frac{37}{3}\approx12.33$ (wrong).
Let's assume they are vertical angles correctly.
$143 - 8x=11x - 12$
$143+12=11x + 8x$
$155 = 19x$
$x=\frac{155}{19}$
$\angle PVS=143-8\times\frac{155}{19}=\frac{143\times19-1240}{19}=\frac{2717 - 1240}{19}=77$

Answer:

$77$