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

Question

Accepted Answer

# Explanation:
## Step1: Use vertical angles property
Vertical angles are equal. So, $5x + 25x+30 = 180$ (linear - pair angles sum to $180^{\circ}$).
$$
\begin{align*}
30x+30&=180\
30x&=180 - 30\
30x&=150\
x&=5
\end{align*}
$$
## Step2: Find $\angle WRS$
$\angle WRS=(25x + 30)^{\circ}$. Substitute $x = 5$ into the expression.
$$
\begin{align*}
\angle WRS&=25\times5+30\
&=125 + 30\
&=155^{\circ}\text{ (This is wrong, we should use the fact that }5x\text{ and }\angle WRS\text{ are vertical angles)}\
\text{Wait, no. Wait, }5x\text{ and }(25x + 30)\text{ are supplementary.}\
\text{We want }\angle WRS = 5x\text{ (vertical angles with the angle opposite to it in the pair)}.\
\text{Since }x = 5\
\angle WRS=5x=5\times5 = 25^{\circ}
\end{align*}
$$

# Answer:
$25^{\circ}$

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QUESTION IMAGE

Question

Explanation:

Step1: Use vertical angles property

Step2: Find \(\angle WRS\)

Answer: