Question

given (mangle qst = 135^{circ}), find the value of (x) using the angle addition postulate. (3x + 1)° (2x - 6)° a (x = 29) b (x = 28) c (x = 26) d (x = 27)

Explanation:

Step1: Apply angle - addition postulate

According to the angle - addition postulate, $m\angle QST=m\angle QSR + m\angle RST$. So, $(3x + 1)+(2x-6)=135$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms: $(3x+2x)+(1 - 6)=135$, which simplifies to $5x-5 = 135$.

Step3: Add 5 to both sides

Add 5 to both sides of the equation: $5x-5 + 5=135 + 5$, resulting in $5x=140$.

Step4: Solve for x

Divide both sides by 5: $\frac{5x}{5}=\frac{140}{5}$, so $x = 28$.

Answer:

B. $x = 28$