Question

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

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, \(5x=25x + 30\) is incorrect. The correct equation should be based on the fact that the sum of angles around a point is \(360^{\circ}\). But if we assume the two given angles are supplementary (a common case in angle - pair problems), we have \(5x+(25x + 30)=180\).

Step2: Simplify the equation

Combine like - terms: \(5x+25x+30 = 180\), which gives \(30x+30 = 180\).
Subtract 30 from both sides: \(30x=180 - 30=150\).

Step3: Solve for \(x\)

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

Step4: Find the measure of \(\angle WRS\)

If we assume \(\angle WRS = 25x+30\), substitute \(x = 5\) into the expression.
\(\angle WRS=25\times5+30=125 + 30=155^{\circ}\). But this is wrong. If we assume \(\angle WRS = 5x\), substituting \(x = 5\) gives \(\angle WRS=25^{\circ}\).

Answer:

C. \(25^{\circ}\)