Question

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

Explanation:

Step1: Set up equation using vertical - angle property

Vertical angles are equal. The angles $(5x)^{\circ}$ and $(25x + 30)^{\circ}$ are vertical angles. So, $5x=25x + 30$.

Step2: Solve the equation for x

Subtract $5x$ from both sides: $0 = 20x+30$. Then subtract 30 from both sides: $- 30=20x$. Divide both sides by 20: $x =-\frac{30}{20}=-1.5$. This is incorrect. We should use the fact that $5x+(25x + 30)=180$ (since they are a linear - pair of angles).
Combining like terms: $30x+30 = 180$.
Subtract 30 from both sides: $30x=150$.
Divide both sides by 30: $x = 5$.

Step3: Find the measure of $\angle WRS$

$\angle WRS=(25x + 30)^{\circ}$. Substitute $x = 5$ into the expression: $25\times5+30=125 + 30=155^{\circ}$ (this is wrong as we mis - identified the angle we need). Since $\angle WRS=(5x)^{\circ}$, substituting $x = 5$ gives $\angle WRS=5\times5 = 25^{\circ}$.

Answer:

$25^{\circ}$