Question

if (mangle klw=(36x + 2)^{circ}), (mangle wlm = 20^{circ}), and (mangle klm=42x + 4), find the measurments down below

Explanation:

Step1: Use angle - addition postulate

Since $\angle KLM=\angle KLW+\angle WLM$, we can set up the equation $42x + 4=(36x + 2)+20$.

Step2: Simplify the right - hand side of the equation

$(36x + 2)+20=36x+22$. So the equation becomes $42x + 4=36x+22$.

Step3: Solve for $x$

Subtract $36x$ from both sides: $42x-36x + 4=36x-36x+22$, which simplifies to $6x+4 = 22$. Then subtract 4 from both sides: $6x+4 - 4=22 - 4$, giving $6x=18$. Divide both sides by 6: $x=\frac{18}{6}=3$.

Step4: Find $m\angle KLW$

Substitute $x = 3$ into the expression for $m\angle KLW$: $m\angle KLW=36x + 2=36\times3+2=108 + 2=110^{\circ}$.

Step5: Find $m\angle KLM$

Substitute $x = 3$ into the expression for $m\angle KLM$: $m\angle KLM=42x + 4=42\times3+4=126+4=130^{\circ}$.

Answer:

$x = 3$
$m\angle KLW=110$
$m\angle KLM=130$