Question

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

Explanation:

Step1: Set up equation

Since vertical - angles are equal, we set $9x + 27=6x + 66$.
$9x-6x=66 - 27$
$3x=39$
$x = 13$.

Step2: Find measure of $\angle RSL$

Substitute $x = 13$ into the expression for $\angle RSL$ which is $9x+27$.
$\angle RSL=9\times13 + 27$
$=117+27$
$=144^{\circ}$

Answer:

D. $144^{\circ}$