Question

1. if (mangle pqt=(3x + 47)^{circ}) and (mangle sqr=(6x - 25)^{circ}), find the measure of (angle sqr).

Explanation:

Step1: Identify vertical - angle relationship

Since $\angle PQT$ and $\angle SQR$ are vertical angles, $m\angle PQT=m\angle SQR$. So, $3x + 47=6x - 25$.

Step2: Solve for $x$

First, move the $x$ - terms to one side: $47 + 25=6x-3x$. Then, $72 = 3x$. Divide both sides by 3: $x=\frac{72}{3}=24$.

Step3: Find the measure of $\angle SQR$

Substitute $x = 24$ into the expression for $m\angle SQR$. $m\angle SQR=(6x - 25)^{\circ}=(6\times24 - 25)^{\circ}=(144 - 25)^{\circ}=119^{\circ}$.

Answer:

$119^{\circ}$