Question

4 fill in the blank 3 points if (mangle rst=(12x - 1)^{circ}), (mangle rsu=(9x - 15)^{circ}), and (mangle ust = 53^{circ}), find each measure.

(x=) type your answer...

(mangle rst=) type your answer...

(mangle rsu=) type your answer...

Explanation:

Step1: Set up the angle - relationship equation

Since $\angle RST=\angle RSU + \angle UST$, we have the equation $(12x - 1)=(9x - 15)+53$.

Step2: Simplify the right - hand side of the equation

$(9x - 15)+53=9x+( - 15 + 53)=9x + 38$. So the equation becomes $12x-1 = 9x + 38$.

Step3: Solve for $x$

Subtract $9x$ from both sides: $12x-9x-1=9x-9x + 38$, which simplifies to $3x-1 = 38$. Then add 1 to both sides: $3x-1 + 1=38 + 1$, so $3x=39$. Divide both sides by 3: $x=\frac{39}{3}=13$.

Step4: Find $m\angle RST$

Substitute $x = 13$ into the expression for $m\angle RST$: $m\angle RST=(12x - 1)=(12\times13-1)=156 - 1=155^{\circ}$.

Step5: Find $m\angle RSU$

Substitute $x = 13$ into the expression for $m\angle RSU$: $m\angle RSU=(9x - 15)=(9\times13-15)=117-15 = 102^{\circ}$.

Answer:

$x = 13$
$m\angle RST=155$
$m\angle RSU = 102$