Question

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

Explanation:

Step1: Identify vertical - angles property

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

Step2: Solve for $x$

Subtract $3x$ from both sides:
$47 = 6x-3x - 25$
$47=3x - 25$
Add 25 to both sides:
$47 + 25=3x$
$72 = 3x$
Divide both sides by 3:
$x=\frac{72}{3}=24$

Step3: Find the measure of $\angle SQR$

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

Answer:

$119^{\circ}$