Question

10 fill in the blank 1 point what is the length of line segment dg? d 2x + 17 e 8 f 2 g x + 20 dg = type your answer..

Explanation:

Step1: Set up an equation

Since $DE + EF+FG=DG$ and also $DG = x + 20$, we have $(2x + 17)+8 + 2=x + 20$.

Step2: Simplify the left - hand side

Combine like terms: $2x+17 + 8+2=2x+(17 + 8+2)=2x + 27$. So the equation becomes $2x+27=x + 20$.

Step3: Solve for x

Subtract x from both sides: $2x - x+27=x - x + 20$, which gives $x+27 = 20$. Then subtract 27 from both sides: $x=20 - 27=-7$.

Step4: Find the length of DG

Substitute $x=-7$ into the expression for DG ($DG=x + 20$). So $DG=-7 + 20 = 13$.

Answer:

13