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 equation

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

Step2: Simplify left - hand side

Combine like terms on the left - hand side: $2x+17 + 8+2=2x+27$. 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 length of DG

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

Answer:

13