Question

solve for x.
(15x - 8)°
(128 - 3x)°
x =

Explanation:

Step1: Assume vertical - angle relationship

If the angles \((15x - 8)^{\circ}\) and \((128 - 3x)^{\circ}\) are vertical angles, they are equal. So we set up the equation \(15x-8 = 128 - 3x\).

Step2: Add \(3x\) to both sides

Adding \(3x\) to both sides of the equation \(15x-8 = 128 - 3x\) gives \(15x+3x - 8=128-3x + 3x\), which simplifies to \(18x-8 = 128\).

Step3: Add 8 to both sides

Adding 8 to both sides of \(18x-8 = 128\) gives \(18x-8 + 8=128 + 8\), resulting in \(18x=136\).

Step4: Solve for \(x\)

Dividing both sides of \(18x = 136\) by 18, we get \(x=\frac{136}{18}=\frac{68}{9}\approx7.56\). But if we assume they are corresponding - angles (assuming \(DE\parallel FG\)), we also set up the equation \(15x-8=128 - 3x\).
Let's assume they are supplementary angles (a common relationship in parallel - line and transversal scenarios). If the sum of the two angles is \(180^{\circ}\), then \((15x - 8)+(128 - 3x)=180\).

Step5: Combine like - terms

Combining like - terms in \((15x - 8)+(128 - 3x)=180\), we have \((15x-3x)+(-8 + 128)=180\), which simplifies to \(12x+120 = 180\).

Step6: Subtract 120 from both sides

Subtracting 120 from both sides gives \(12x+120-120 = 180-120\), so \(12x=60\).

Step7: Solve for \(x\)

Dividing both sides by 12, we get \(x = 5\).

Answer:

\(x = 5\)