Question

given ( m parallel n ), find the value of ( x ) and ( y ).

Explanation:

Step1: Find the value of \(x\)

Since \(m\parallel n\), then \(3x - 19=2x + 1\) (alternate - interior angles are equal).
Subtract \(2x\) from both sides: \(3x-2x-19=2x - 2x+1\), so \(x-19 = 1\).
Add 19 to both sides: \(x=1 + 19\), so \(x = 20\).

Step2: Find the value of \(y\)

Substitute \(x = 20\) into \(3x-19\): \(3\times20-19=60 - 19=41^{\circ}\).
Since \(m\parallel n\), \(3x - 19\) and \(5y+19\) are supplementary (same - side interior angles). So \(3x-19+5y + 19=180\).
Simplify to \(3x+5y=180\). Substitute \(x = 20\): \(3\times20+5y=180\), \(60+5y=180\).
Subtract 60 from both sides: \(5y=180 - 60\), \(5y=120\).
Divide both sides by 5: \(y=\frac{120}{5}=24\).

Answer:

\(x = 20\), \(y = 24\)