Question

1. given $overline{rvu}$, $overline{ru}perpoverline{sv}$, $mangle svt=(8x + 5)^{circ}$, and $mangle tvu=(3x + 8)^{circ}$. what is the measure of $angle svt$?

Explanation:

Step1: Use angle - addition property

Since $\overline{RU}\perp\overline{SV}$, $\angle RSV = 90^{\circ}$, and $\angle SVT+\angle TVU=\angle RSV = 90^{\circ}$. So, $(8x + 5)+(3x + 8)=90$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms: $8x+3x+5 + 8=90$, which simplifies to $11x+13 = 90$.

Step3: Solve for $x$

Subtract 13 from both sides: $11x=90 - 13=77$. Then divide both sides by 11: $x=\frac{77}{11}=7$.

Step4: Find the measure of $\angle SVT$

Substitute $x = 7$ into the expression for $m\angle SVT$. $m\angle SVT=(8x + 5)^{\circ}$. So, $m\angle SVT=8\times7+5=56 + 5=61^{\circ}$.

Answer:

$61^{\circ}$