Question

lines $l$, $m$, and $n$ are parallel and cut by transversal $p$.

enter the values of $x$ and $y$.

the value of $x$ 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 same - side interior angles is \(180^{\circ}\).
We have \(108+(3x - 6)=180\).
Simplify the left - hand side: \(108+3x-6 = 3x + 102\).
So, \(3x+102 = 180\).
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 \(2y\) 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 \(26\) and the value of \(y\) is \(36\).