Question

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

Explanation:

Step1: Assume vertical - angle relationship

Let's assume that the angle $(2x + 30)^{\circ}$ and the $105^{\circ}$ angle are vertical angles. Vertical angles are equal. So we set up the equation $2x+30 = 105$.

Step2: Solve the equation for $x$

Subtract 30 from both sides of the equation: $2x=105 - 30$. So $2x = 75$. Then divide both sides by 2: $x=\frac{75}{2}=37.5$.

Step3: Find the measure of $\angle WRS$

If we assume $\angle WRS=x$, then $\angle WRS = 37.5^{\circ}$.

Answer:

D. $37.5^{\circ}$