Question

Question was provided via image upload.

Explanation:

Step1: Solve for \(x\)

Vertical angles are equal. So \(3x + 8=5x - 20\).
Subtract \(3x\) from both sides: \(8 = 2x-20\).
Add \(20\) to both sides: \(28=2x\).
Divide by \(2\): \(x = 14\).

Step2: Solve for \(y\)

Supplementary angles sum to \(180^{\circ}\).
Substitute \(x = 14\) into \(3x + 8\) and \(5x + 4y\).
\(3x+8=3\times14 + 8=42 + 8=50^{\circ}\).
Since \(3x + 8+(5x + 4y)=180\), substitute \(x = 14\):
\(50+(5\times14+4y)=180\).
\(50 + 70+4y=180\).
\(120+4y=180\).
Subtract \(120\): \(4y=60\).
Divide by \(4\): \(y = 15\).

Answer:

\(x = 14\), \(y = 15\)