Question

if the measure of <rst is 134 degrees, find the measure of <qst.
(3x - 1)°
(x - 1)°
34 degrees
33 degrees
67 degrees
98 degrees

Explanation:

Step1: Set up an equation

Since $\angle RST=(3x - 1)^{\circ}+(x - 1)^{\circ}$ and $\angle RST = 134^{\circ}$, we have $(3x - 1)+(x - 1)=134$.

Step2: Simplify the left - hand side

Combine like terms: $3x+x-1 - 1=134$, which gives $4x-2 = 134$.

Step3: Solve for $x$

Add 2 to both sides: $4x=134 + 2=136$. Then divide both sides by 4, so $x=\frac{136}{4}=34$.

Step4: Find the measure of $\angle QST$

$\angle QST=(x - 1)^{\circ}$. Substitute $x = 34$ into it, we get $\angle QST=(34 - 1)^{\circ}=33^{\circ}$.

Answer:

33 degrees