Question

find (xy).
1.
2.
3.
4.
find the value (x).
5.
6.
7.
8.

Explanation:

Step1: Use segment - addition postulate for problem 1

Since \(XY = XZ+ZY\), and \(XZ = 7\), \(ZY = 9\), then \(XY=7 + 9\).

Step2: Calculate the value of \(XY\) for problem 1

\(XY=16\)

Step3: Use segment - addition postulate for problem 2

We know that \(ZY=ZX + XY\), given \(ZY = 12\), \(ZX = 5\), then \(12=5+XY\), so \(XY=12 - 5\).

Step4: Calculate the value of \(XY\) for problem 2

\(XY = 7\)

Step5: Use segment - addition postulate for problem 3

Given \(XZ=XY + YZ\), \(XZ = 24\), \(YZ = 8\), then \(XY=XZ - YZ\).

Step6: Calculate the value of \(XY\) for problem 3

\(XY=24 - 8=16\)

Step7: Use segment - addition postulate for problem 4

Given \(XZ=XY + YZ\), \(XZ = 12\), \(YZ = 3\), then \(XY=XZ - YZ\).

Step8: Calculate the value of \(XY\) for problem 4

\(XY=12 - 3 = 9\)

Step9: Use segment - addition postulate for problem 5

Since \(AB=AC + CB\), \(AB = 36\), \(AC = 6\), \(CB=2x + 10\), we have the equation \(36=6+(2x + 10)\).
First, simplify the right - hand side: \(36=2x+16\).
Then, subtract 16 from both sides: \(2x=36 - 16=20\).
Finally, divide both sides by 2: \(x = 10\).

Step10: Use segment - addition postulate for problem 6

Since \(DF=DE + EF\), \(DF = 40\), \(DE = 22\), \(EF=3x - 6\), we have the equation \(40=22+(3x - 6)\).
First, simplify the right - hand side: \(40=3x + 16\).
Then, subtract 16 from both sides: \(3x=40 - 16 = 24\).
Finally, divide both sides by 3: \(x = 8\).

Step11: Use segment - addition postulate for problem 7

Since \(JL=JK + KL\), \(JL = 8x\), \(JK = 20\), \(KL = 4\), we have the equation \(8x=20 + 4\).
Simplify the right - hand side: \(8x=24\).
Divide both sides by 8: \(x = 3\).

Step12: Use segment - addition postulate for problem 8

Since \(GI=GH+HI\), \(GI=-10 + 20x\), \(GH = 8\), \(HI=5x - 3\), we have the equation \(-10 + 20x=8+(5x - 3)\).
First, simplify the right - hand side: \(-10 + 20x=5x + 5\).
Subtract \(5x\) from both sides: \(20x-5x=5 + 10\).
Combine like terms: \(15x=15\).
Divide both sides by 15: \(x = 1\).

Answer:

1. \(XY = 16\)
2. \(XY = 7\)
3. \(XY = 16\)
4. \(XY = 9\)
5. \(x = 10\)
6. \(x = 8\)
7. \(x = 3\)
8. \(x = 1\)