Question

ch. 1.2 - segment addition postulate
refer to the figures below and the given information to find each measure.
given: dg = 60ft
d 4x - 3 o 2x + 21 g
x =
do =
og =

Explanation:

Step1: Apply segment - addition postulate

Since $DG = DO+OG$, we have $(4x - 3)+(2x + 21)=60$.

Step2: Combine like - terms

$4x+2x-3 + 21=60$, which simplifies to $6x+18 = 60$.

Step3: Isolate the variable term

Subtract 18 from both sides: $6x=60 - 18$, so $6x=42$.

Step4: Solve for x

Divide both sides by 6: $x=\frac{42}{6}=7$.

Step5: Find DO

Substitute $x = 7$ into the expression for DO: $DO=4x-3=4\times7-3=28 - 3=25$.

Step6: Find OG

Substitute $x = 7$ into the expression for OG: $OG=2x + 21=2\times7+21=14 + 21=35$.

Answer:

$x = 7$
$DO = 25$
$OG = 35$