Question

refer to the figure and the given information to find each measure. 9. given: ac = 39 m. a - 2x - 8, b. x + 17, c. 10. given the figure and dg = 60 ft. d 4x - 3, o 2x + 21, g. ab = _, bc = _, x = _, dg = _, og = _

Explanation:

Step1: Use segment - addition postulate

Since $AC = AB+BC$, and $AB = 2x - 8$, $BC=x + 17$, $AC = 39$. We substitute these values into the equation: $(2x - 8)+(x + 17)=39$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $2x-8+x + 17=3x + 9$. So, $3x+9 = 39$.

Step3: Solve for $x$

Subtract 9 from both sides: $3x=39 - 9=30$. Then divide both sides by 3: $x = 10$.

Step4: Find $AB$

Substitute $x = 10$ into the expression for $AB$: $AB=2x-8=2\times10 - 8=12$.

Step5: Find $BC$

Substitute $x = 10$ into the expression for $BC$: $BC=x + 17=10+17=27$.

For the second part (about $DOQ$):

Step1: Use segment - addition postulate

Since $DQ=DO+OG$, and $DO = 4x-3$, $OG=2x + 21$, $DQ = 60$. We substitute these values into the equation: $(4x-3)+(2x + 21)=60$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $4x-3+2x + 21=6x+18$. So, $6x + 18=60$.

Step3: Solve for $x$

Subtract 18 from both sides: $6x=60 - 18 = 42$. Then divide both sides by 6: $x = 7$.

Step4: Find $DO$

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

Step5: Find $OG$

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

Answer:

For the first part: $x = 10$, $AB = 12$, $BC = 27$.
For the second part: $x = 7$, $DO = 25$, $OG = 35$.