Question

question 7 of 10
what is the measure of ∠rsl?
(9x + 27)°
(6x + 66)°
a. 144°
b. 146°
c. 142°
d. 140°

Explanation:

Step1: Set up equation

Vertical - angles are equal. So, $9x + 27=6x + 66$.

Step2: Solve for x

Subtract $6x$ from both sides: $9x-6x + 27=6x-6x + 66$, which simplifies to $3x+27 = 66$. Then subtract 27 from both sides: $3x+27 - 27=66 - 27$, giving $3x=39$. Divide both sides by 3: $x = 13$.

Step3: Find the measure of ∠RSL

Substitute $x = 13$ into the expression for ∠RSL, which is $9x + 27$. So, $9(13)+27=117 + 27=144$.

Answer:

A. $144^{\circ}$