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 (27)

Explanation:

Step1: Use the property of consecutive interior angles

Since lines \(l\) and \(m\) are parallel and cut by transversal \(p\), the sum of the consecutive - interior angles is \(180^{\circ}\).
So, \(108+(3x - 6)=180\).
Simplify the left - hand side: \(108+3x-6 = 3x + 102\).
Then the equation becomes \(3x+102 = 180\).
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 corresponding angles are equal.
The angle of \(108^{\circ}\) and \((2y)^{\circ}\) are supplementary (they form a linear pair with the angle that is corresponding to \(108^{\circ}\)).
Another way is to use the property that the angle adjacent to \(108^{\circ}\) (which is \(180 - 108=72^{\circ}\)) and \((2y)^{\circ}\) are corresponding angles. So \(2y=72\).
Divide both sides by \(2\): \(y = 36\).

Answer:

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