Question

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

Explanation:

Step1: Set up equation using linear - pair property

Since $\angle TRV$ and $\angle WR S$ are vertical angles, and $\angle TRV$ and $\angle VRW$ form a linear - pair, we know that $\angle TRV+\angle VRW = 180^{\circ}$. Also, $\angle TRV = 5x$ and $\angle VRW=25x + 30$. So, $5x+(25x + 30)=180$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $5x+25x+30 = 30x+30$. So the equation becomes $30x + 30=180$.

Step3: Solve for $x$

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

Step4: Find the measure of $\angle WRS$

Since $\angle WRS=\angle TRV$ (vertical angles are equal) and $\angle TRV = 5x$, substitute $x = 5$ into $5x$. So $\angle WRS=5\times5 = 25^{\circ}$.

Answer:

$25^{\circ}$