in the diagram, what is the measure of ∠wrs? 5° 7.5° 25° 37.5° (5x)° (25x + 30)°

Explanation:

Step1: Set up equation

Since $\angle TRV$ and $\angle WRS$ are vertical - angles, they are equal. Also, $\angle TRV+\angle VRZ = 180^{\circ}$ (a straight - line angle), and $\angle VRZ=(25x + 30)^{\circ}$, $\angle TRV=(5x)^{\circ}$. So, $5x+(25x + 30)=180$.

Step2: Simplify the equation

Combine like terms: $30x+30 = 180$.

Step3: Solve for x

Subtract 30 from both sides: $30x=180 - 30=150$. Then divide both sides by 30: $x = 5$.

Step4: Find the measure of $\angle WRS$

Since $\angle WRS=\angle TRV$ and $\angle TRV=(5x)^{\circ}$, substitute $x = 5$ into the expression for $\angle TRV$. So, $\angle WRS=5\times5 = 25^{\circ}$.

Answer:

$25^{\circ}$