Question

(9x + 12)
(4y - 10)
3x
x:
y:

Explanation:

Step1: Solve for \(x\)

Since \(9x + 12\) and \(3x\) are supplementary angles (they form a linear pair), we know that \(9x+12 + 3x=180\).
Combine like - terms: \(12x+12 = 180\).
Subtract 12 from both sides: \(12x=180 - 12=168\).
Divide both sides by 12: \(x=\frac{168}{12}=14\).

Step2: Solve for \(y\)

Assume \(3x\) and \(4y - 10\) are vertical angles (equal in measure).
Since \(x = 14\), then \(3x=3\times14 = 42\).
Set \(4y-10 = 42\).
Add 10 to both sides: \(4y=42 + 10=52\).
Divide both sides by 4: \(y=\frac{52}{4}=13\).

Answer:

\(x = 14\), \(y = 13\)