Question

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

Explanation:

Step1: Find the value of \(x\)

Since \(m\parallel n\), the angle \((3x - 20)^{\circ}\) and \((2x + 3)^{\circ}\) are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal. So we have the equation \(3x-20=2x + 3\).
Subtract \(2x\) from both sides: \(3x-2x-20=2x-2x + 3\), which gives \(x-20=3\).
Add \(20\) to both sides: \(x=3 + 20=23\).

Step2: Find the value of \(y\)

The angle \((3x - 20)^{\circ}\) and \((y - 6)^{\circ}\) are supplementary (they form a linear pair).
First, substitute \(x = 23\) into \((3x - 20)^{\circ}\): \(3\times23-20=69 - 20=49^{\circ}\).
Since \((3x - 20)+(y - 6)=180\) (linear - pair angles), substitute \(3x - 20 = 49\) into the equation: \(49+(y - 6)=180\).
Simplify the left - hand side: \(y+43 = 180\).
Subtract \(43\) from both sides: \(y=180 - 43=107\).

Answer:

$x = 23$, $y = 107$