Question

lines ( ell ), ( m ), and ( n ) are parallel and cut by transversal ( p ).

enter the values of ( x ) and ( y ).

the value of ( x ) is

the value of ( y ) is

Explanation:

Step1: Use the property of same - side interior angles

Since lines \(l\) and \(m\) are parallel and cut by transversal \(p\), the sum of the angle \(108^{\circ}\) and \((3x - 6)^{\circ}\) is \(180^{\circ}\) (same - side interior angles).
So, \(108+(3x - 6)=180\).
Simplify the left - hand side: \(108+3x-6 = 3x + 102\).
Then \(3x+102 = 180\).
Subtract \(102\) from both sides: \(3x=180 - 102\), \(3x = 78\).
Divide both sides by \(3\): \(x=\frac{78}{3}=26\).

Step2: Use the property of corresponding angles

Since lines \(l\) and \(n\) are parallel and cut by transversal \(p\), the angle \((2y)^{\circ}\) and the angle adjacent to \(108^{\circ}\) (which is \(180 - 108=72^{\circ}\)) are corresponding angles.
So, \(2y=72\).
Divide both sides by \(2\): \(y = 36\).

Answer:

The value of \(x\) is \(26\).
The value of \(y\) is \(36\).