Question

sc 2: i can use angle addition and line segment addition to analyze line - segments, adjacent angles, and linear pairs of angles. 2a) how long is $overline{vw}$? (your answer will not have “x” in it.) t 32 3x v x + 8 w 2b) m is the mid - point of $overline{ln}$. how long is $overline{ln}$? (your answer will not have “x” in it.) l 11x - 21 m 8x + 15 n

Explanation:

Step1: Set up equation for 2a

Since $TV + VW=TW$, we have $3x+(x + 8)=32$.
Combining like - terms gives $4x+8 = 32$.
Subtract 8 from both sides: $4x=32 - 8=24$.
Divide both sides by 4: $x = 6$.

Step2: Find length of $\overline{VW}$

Substitute $x = 6$ into the expression for $VW$ which is $x + 8$.
So $VW=6 + 8=14$.

Step3: Set up equation for 2b

Since $M$ is the mid - point of $\overline{LN}$, then $LM=MN$.
So $11x-21=8x + 15$.
Subtract $8x$ from both sides: $11x-8x-21=8x-8x + 15$, which simplifies to $3x-21=15$.
Add 21 to both sides: $3x=15 + 21=36$.
Divide both sides by 3: $x = 12$.

Step4: Find length of $\overline{LN}$

First find $LM$ or $MN$ by substituting $x = 12$ into either expression. Let's use $LM=11x-21$.
$LM=11\times12-21=132-21 = 111$.
Since $LN=LM + MN$ and $LM = MN$, then $LN=2LM$.
So $LN=2\times111 = 222$.

Answer:

2a) 14
2b) 222