Question

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

Explanation:

Step1: Set up equation using linear - pair property

Since $\angle TRV$ and $\angle WRS$ are vertical angles, and $\angle TRV$ and $(25x + 30)^{\circ}$ form a linear - pair (sum is $180^{\circ}$), and $\angle TRV=5x^{\circ}$, we have the equation $5x+(25x + 30)=180$.

Step2: Combine like - terms

Combining the $x$ terms on the left - hand side gives $30x+30 = 180$.

Step3: Isolate the variable term

Subtract 30 from both sides: $30x=180 - 30=150$.

Step4: Solve for $x$

Divide both sides by 30: $x=\frac{150}{30}=5$.

Step5: Find the measure of $\angle WRS$

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

Answer:

$25^{\circ}$