If two parallel lines are intersected by a transversal, and angles are marked as x degrees, 3x degrees, and y degrees, find the value of y.

The angle marked $x^\circ$ is an exterior angle. The angle vertically opposite to this $x^\circ$ is an interior angle on line $l_1$ to the left of the transversal $l_3$. This interior angle also measures $x^\circ$.
The angle marked $3x^\circ$ is an interior angle on line $l_2$ to the right of the transversal $l_3$.
Since $l_1 \parallel l_2$, the interior angle $x^\circ$ (on $l_1$ to the left) and the interior angle $3x^\circ$ (on $l_2$ to the right) are consecutive interior angles (also known as same-side interior angles). The sum of consecutive interior angles is $180^\circ$.

$$x^\circ + 3x^\circ = 180^\circ$$

Combine the terms:

$$4x^\circ = 180^\circ$$

Divide by 4:

$$x^\circ = \frac{180^\circ}{4}$$ $$x^\circ = 45^\circ$$

The angle $y^\circ$ is an interior angle on line $l_1$ to the right of the transversal $l_3$.
The interior angle $x^\circ$ (on $l_1$ to the left of $l_3$, which is vertically opposite to the given exterior $x^\circ$) and $y^\circ$ form a linear pair on line $l_1$. The sum of angles in a linear pair is $180^\circ$.

$$x^\circ + y^\circ = 180^\circ$$

Substitute the value of $x^\circ$ found in Step 2 into the equation:

$$45^\circ + y^\circ = 180^\circ$$

Subtract $45^\circ$ from both sides:

$$y^\circ = 180^\circ - 45^\circ$$ $$y^\circ = 135^\circ$$

The value of $y$ is 135.