Question

in the diagram, what is the measure of ∠wrs? 5° 7.5° 25° 37.5° (diagram shows point r with lines, angles (5x)° and (25x + 30)°)

Explanation:

Step1: Identify supplementary angles

Angles \( (5x)^\circ \) and \( (25x + 30)^\circ \) are supplementary (they form a linear pair), so their sum is \( 180^\circ \).
\[
5x + (25x + 30) = 180
\]

Step2: Solve for \( x \)

Combine like terms:
\[
30x + 30 = 180
\]
Subtract 30 from both sides:
\[
30x = 150
\]
Divide by 30:
\[
x = 5
\]

Step3: Find \( \angle WRS \)

\( \angle WRS \) is equal to \( (5x)^\circ \) (vertical angles or alternate angles, depending on the diagram). Substitute \( x = 5 \):
\[
5x = 5 \times 5 = 25
\]

Answer:

\( 25^\circ \) (corresponding to the option "25°")