Question

1. using the figure below solve for m∠lik. m∠jil = 20x - 10 m∠lik = 8x - 20 m∠jik = 140 - 6x

Explanation:

Step1: Use angle - addition postulate

Since $\angle{JIL}+\angle{LIK}=\angle{JIK}$, we substitute the given angle - measures: $(20x - 10)+(8x - 20)=140 - 6x$.

Step2: Simplify the left - hand side

Combine like terms: $20x+8x-10 - 20=28x - 30$. So, $28x - 30=140 - 6x$.

Step3: Solve for x

Add $6x$ to both sides: $28x+6x-30=140 - 6x+6x$, which gives $34x - 30=140$. Then add 30 to both sides: $34x-30 + 30=140 + 30$, so $34x=170$. Divide both sides by 34: $x = 5$.

Step4: Find $m\angle{LIK}$

Substitute $x = 5$ into the expression for $m\angle{LIK}$. $m\angle{LIK}=8x - 20$. Replace $x$ with 5: $m\angle{LIK}=8\times5-20$.
$m\angle{LIK}=40 - 20$.
$m\angle{LIK}=20^{\circ}$.

Answer:

$20^{\circ}$