Question

1. p i g pi = 2x ig = 18 pg = 34 find pi 6. y e a ea = 8y + 4 ye = 4y + 8 ya = 15y - 9 find y find ea 9. m∠efg = 112° and m∠efa = 80°. find m∠aeg

Explanation:

Step1: Use segment - addition postulate for the first problem

Since \(PG = PI+IG\), and \(PI = 2x\), \(IG = 18\), \(PG = 34\), we substitute the values into the equation: \(2x+18 = 34\).

Step2: Solve the equation for \(x\)

Subtract 18 from both sides of the equation \(2x+18 = 34\): \(2x=34 - 18\), so \(2x = 16\). Then divide both sides by 2: \(x=\frac{16}{2}=8\).

Step3: Find \(PI\)

Since \(PI = 2x\) and \(x = 8\), then \(PI=2\times8 = 16\).

Step4: Use segment - addition postulate for the second problem

Since \(YA=YE + EA\), and \(EA = 8y + 4\), \(YE = 4y + 8\), \(YA = 15y-9\), we substitute the values into the equation: \((4y + 8)+(8y + 4)=15y-9\).

Step5: Simplify the left - hand side of the equation

Combine like terms: \(4y+8y+8 + 4=12y + 12\). So the equation becomes \(12y+12 = 15y-9\).

Step6: Solve the equation for \(y\)

Subtract \(12y\) from both sides: \(12=15y-12y-9\), which simplifies to \(12 = 3y-9\). Then add 9 to both sides: \(12 + 9=3y\), so \(21 = 3y\). Divide both sides by 3: \(y = 7\).

Step7: Find \(EA\)

Since \(EA = 8y+4\) and \(y = 7\), then \(EA=8\times7 + 4=56 + 4=60\).

Answer:

For the first problem, \(PI = 16\).
For the second problem, \(y = 7\) and \(EA = 60\).