Question

question 5 if the measure of <rst is 134 degrees, find the measure of <qst.

Explanation:

Step1: Set up an equation

We know that $\angle RST=(3x - 1)^{\circ}$ and $\angle QST=(x - 1)^{\circ}$, and $\angle RST=\angle RSQ+\angle QST$. So $(3x - 1)=(x - 1)+\angle RSQ$. Also, we are given that $\angle RST = 134^{\circ}$, so $3x-1=134$.

Step2: Solve for $x$

Add 1 to both sides of the equation $3x - 1=134$:
$3x=134 + 1=135$.
Then divide both sides by 3: $x=\frac{135}{3}=45$.

Step3: Find the measure of $\angle QST$

Substitute $x = 45$ into the expression for $\angle QST$. $\angle QST=(x - 1)^{\circ}$. So $\angle QST=(45-1)^{\circ}=44^{\circ}$. But there seems to be a misunderstanding in the problem - setup above. If we assume $\angle RST$ is the sum of two non - overlapping angles where $\angle RST=(3x - 1)^{\circ}$ and $\angle QST=(x - 1)^{\circ}$ and $\angle RST = 134^{\circ}$.
We know that $\angle RST=\angle RSQ+\angle QST$. So $3x-1=(x - 1)+\angle QST$.
Since $\angle RST = 134^{\circ}$, we have $3x-1=134$, $3x=135$, $x = 45$. Then $\angle QST=x - 1=45-1 = 44^{\circ}$ which is not in the options. Let's assume $\angle RST$ is composed of two angles such that $\angle RST=\angle RSQ+\angle QST$ and we know $\angle RST = 134^{\circ}$. If we assume $\angle RSQ = 3x-1$ and $\angle QST=x - 1$ and $\angle RST=\angle RSQ+\angle QST$, then $3x-1+x - 1=134$.
Combining like terms: $4x-2 = 134$.
Add 2 to both sides: $4x=136$.
Divide by 4: $x = 34$.
Then $\angle QST=x - 1=34 - 1=33^{\circ}$.

Answer:

B. 33 degrees