Question

solve for x and the measure of < arl.
answer attempt 2 out of 5
x = 11
m < arl = 18°

Explanation:

Step1: Identify angle - relationship

Since $\angle ARL$ and $\angle CSR$ are vertical angles, they are equal. So $3x - 15=x + 7$.

Step2: Solve for x

Subtract x from both sides: $3x-x-15=x - x+7$, which simplifies to $2x-15 = 7$. Then add 15 to both sides: $2x-15 + 15=7 + 15$, getting $2x=22$. Divide both sides by 2: $x=\frac{22}{2}=11$.

Step3: Find the measure of $\angle ARL$

Substitute $x = 11$ into the expression for $\angle ARL$ which is $3x-15$. So $m\angle ARL=3\times11 - 15=33 - 15=18^{\circ}$.

Answer:

$x = 11$
$m\angle ARL=18^{\circ}$