Question

in the diagram, what is the measure of \\( \angle wrs \\)?
\\( 5 ^ { \circ } \\)
\\( 7.5 ^ { \circ } \\)
\\( 25 ^ { \circ } \\)
\\( 37.5 ^ { \circ } \\)

Explanation:

Step1: Use the property of linear pair

Angles \((5x)^{\circ}\) and \((25x + 30)^{\circ}\) form a linear pair. So, \(5x+25x + 30=180\).

Step2: Solve the equation for \(x\)

Combine like - terms: \(30x+30 = 180\). Subtract 30 from both sides: \(30x=180 - 30=150\). Divide both sides by 30: \(x = 5\).

Step3: Find the measure of \(\angle WRS\)

Since \(\angle WRS=(5x)^{\circ}\), substitute \(x = 5\) into \(5x\). Then \(5x=5\times5 = 25\). So, \(\angle WRS = 25^{\circ}\).

Answer:

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