in the diagram, what is the measure of ∠wrs? 5° 7.5° 25° 37.5°

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle VRT$ and $\angle WRS$ are vertical angles. So $5x=25x - 30$.

Step2: Solve the equation for $x$

Subtract $5x$ from both sides: $0 = 25x-5x - 30$, which simplifies to $0 = 20x - 30$. Then add 30 to both sides: $30 = 20x$. Divide both sides by 20: $x=\frac{30}{20}=1.5$.

Step3: Find the measure of $\angle WRS$

Substitute $x = 1.5$ into the expression for $\angle WRS$ (we can use either $5x$ or $25x - 30$). Using $5x$, we get $5\times1.5 = 7.5^{\circ}$.

Answer:

$7.5^{\circ}$