Question

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

Explanation:

Step1: Use the linear - pair relationship

Since \((6x - 2)^{\circ}\) and \((3x+2)^{\circ}\) form a linear pair, their sum is \(180^{\circ}\).
So, \((6x - 2)+(3x + 2)=180\).
Simplify the left - hand side: \(6x-2 + 3x+2=9x\).
Then \(9x=180\).
Solve for \(x\): \(x=\frac{180}{9}=20\).

Step2: Use the corresponding - angles relationship

When \(m\parallel n\), \(y^{\circ}\) and \((6x - 2)^{\circ}\) are corresponding angles.
Substitute \(x = 20\) into \((6x - 2)\): \(6x-2=6\times20 - 2=120 - 2 = 118\).
So \(y = 118\).

Answer:

\(x = 20\), \(y=118\)