Question

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

Explanation:

Step1: Set the two angle - measures equal

Since $\angle PQT$ and $\angle SQR$ are vertical angles and vertical angles are equal, we set up the equation $3x + 47=6x - 25$.

Step2: Solve for $x$

First, subtract $3x$ from both sides: $47 = 6x-3x - 25$, which simplifies to $47 = 3x-25$. Then add 25 to both sides: $47 + 25=3x$, so $72 = 3x$. Divide both sides by 3: $x=\frac{72}{3}=24$.

Step3: Find the measure of $\angle SQR$

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

Answer:

$119^{\circ}$