Question

1. if $overline{sv} perp overline{rt}$, $mangle rsu=(17x - 3)^{circ}$, and $mangle ust=(6x - 1)^{circ}$, find each missing measure.

Explanation:

Step1: Use perpendicular - angle property

Since $\overline{SV}\perp\overline{RT}$, $\angle RSU+\angle UST = 90^{\circ}$. So, $(17x - 3)+(6x - 1)=90$.

Step2: Combine like - terms

$17x+6x-3 - 1=90$, which simplifies to $23x-4 = 90$.

Step3: Add 4 to both sides

$23x=90 + 4$, so $23x=94$.

Step4: Solve for x

$x=\frac{94}{23}$.

Step5: Find $m\angle RSU$

Substitute $x = \frac{94}{23}$ into $m\angle RSU=(17x - 3)$.
$m\angle RSU=17\times\frac{94}{23}-3=\frac{1598}{23}-\frac{69}{23}=\frac{1598 - 69}{23}=\frac{1529}{23}\approx66.48^{\circ}$.

Step6: Find $m\angle UST$

Substitute $x=\frac{94}{23}$ into $m\angle UST=(6x - 1)$.
$m\angle UST=6\times\frac{94}{23}-1=\frac{564}{23}-\frac{23}{23}=\frac{564 - 23}{23}=\frac{541}{23}\approx23.52^{\circ}$.

Answer:

$x=\frac{94}{23}$, $m\angle RSU=\frac{1529}{23}\approx66.48^{\circ}$, $m\angle UST=\frac{541}{23}\approx23.52^{\circ}$