Question

solve for x and the measure of < arl.
answer attempt 3 out of 5
x =
m < arl =
(3x - 15)°
(x + 7)°

Explanation:

Step1: Set up equation

Since $\angle ARL$ and $\angle CSD$ are vertical - angles and vertical angles are equal, we set up the equation $3x−15=x + 7$.

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: $2x−15 + 15=7 + 15$, giving $2x=22$. 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, $m\angle ARL=3\times11−15=33 - 15=18$.

Answer:

$x = 11$
$m\angle ARL=18$