Question

find the length indicated. 17) find gf
g • 13 + x • f x + 15 • e
18
13 + y + x + 15 = 18
2x + 28 = 18

• 28 - 28

-2x = -10
-2 - 2
x = 5

Explanation:

Step1: Set up the equation

Since $GF + FE=GE$, we have $(13 + x)+(x + 15)=18$.

Step2: Simplify the left - hand side

Combining like terms, we get $13+x+x + 15=2x+28$. So the equation becomes $2x + 28=18$.

Step3: Isolate the variable term

Subtract 28 from both sides: $2x+28 - 28=18 - 28$, which simplifies to $2x=-10$.

Step4: Solve for x

Divide both sides by 2: $\frac{2x}{2}=\frac{-10}{2}$, so $x = - 5$.

Step5: Find the length of GF

Substitute $x=-5$ into the expression for $GF$ which is $13 + x$. Then $GF=13+( - 5)=8$.

Answer:

8