Question

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

Explanation:

Step1: Find the value of \(x\)

Since \(m\parallel n\), the angles \((3x - 19)^{\circ}\) and \((2x + 1)^{\circ}\) are equal (alternate interior angles).
So, \(3x-19=2x + 1\).
Subtract \(2x\) from both sides: \(3x-2x-19=2x-2x + 1\), which gives \(x-19=1\).
Add \(19\) to both sides: \(x-19 + 19=1+19\), so \(x = 20\).

Step2: Find the value of \(y\)

Substitute \(x = 20\) into \((3x - 19)^{\circ}\), we get \(3\times20-19=60 - 19=41^{\circ}\).
Since \(m\parallel n\), \((3x - 19)^{\circ}\) and \((5y + 19)^{\circ}\) are supplementary (same - side interior angles).
So, \((3x - 19)+(5y + 19)=180\).
Substitute \(x = 20\) into the equation: \(41+(5y + 19)=180\).
Simplify the left - hand side: \(5y+60 = 180\).
Subtract \(60\) from both sides: \(5y+60 - 60=180 - 60\), which gives \(5y=120\).
Divide both sides by \(5\): \(y=\frac{120}{5}=14\).

Answer:

\(x = 20\), \(y = 14\)