Question

1. if m∠rst=(12x - 1)°, m∠rsu=(9x - 15)°, and m∠ust = 53°, find each measure.

x =

m∠rst =

m∠rsu =

Explanation:

Step1: Use angle - addition postulate

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: Isolate the variable $x$

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: $x = 13$.

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:

$x = 13$
$m\angle RST=155^{\circ}$
$m\angle RSU=102^{\circ}$