Question

1. if sv ⊥ rt, m∠rsu=(17x - 3)°, and m∠ust=(6x - 1)°, find each missing measure.

x =
m∠rsu =
m∠ust =
m∠wsv =
m∠vsu =

Explanation:

Step1: Use the fact that $\angle RSU$ and $\angle UST$ are complementary since $SV\perp RT$.

$m\angle RSU + m\angle UST=90^{\circ}$
$(17x - 3)+(6x - 1)=90$

Step2: Combine like - terms.

$17x+6x-3 - 1 = 90$
$23x-4 = 90$

Step3: Add 4 to both sides of the equation.

$23x=90 + 4$
$23x=94$

Step4: Solve for x.

$x=\frac{94}{23}\approx4.09$

Step5: Find $m\angle RSU$.

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

Step6: Find $m\angle UST$.

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

Step7: Since $\angle VSU$ and $\angle RSU$ are vertical angles, $m\angle VSU=m\angle RSU$.

$m\angle VSU=\frac{1529}{23}\approx66.48^{\circ}$

Step8: Since $\angle WSV$ and $\angle UST$ are vertical angles, $m\angle WSV=m\angle UST$.

$m\angle WSV=\frac{541}{23}\approx23.52^{\circ}$

Answer:

$x=\frac{94}{23}$
$m\angle RSU=\frac{1529}{23}^{\circ}$
$m\angle UST=\frac{541}{23}^{\circ}$
$m\angle VSU=\frac{1529}{23}^{\circ}$
$m\angle WSV=\frac{541}{23}^{\circ}$