10. point q is equidistant from the sides of ∠tsr. find m∠rst.
(2x + 5)°
(5x - 25)°
50°
25°
10°
20°

Question

Accepted Answer

# Answer:
50°
# Explanation:
## Step1: Use the Angle Bisector Theorem
Since point $Q$ is equidistant from the sides of $\angle TSR$, $SQ$ is the angle bisector of $\angle TSR$. So $2x + 5=5x-25$.
## Step2: Solve the equation for $x$
$$
\begin{align*}
2x+5&=5x - 25\
2x-5x&=-25 - 5\
-3x&=-30\
x& = 10
\end{align*}
$$
## Step3: Calculate $\angle RST$
$\angle RST=(2x + 5)+(5x-25)$. Substitute $x = 10$ into the expression:
$$
\begin{align*}
\angle RST&=(2\times10 + 5)+(5\times10-25)\
&=(20 + 5)+(50-25)\
&=25+25\
&=50^{\circ}
\end{align*}
$$

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QUESTION IMAGE

Question

Explanation:

Step1: Use the Angle Bisector Theorem

Step2: Solve the equation for \(x\)

Step3: Calculate \(\angle RST\)

Answer: