Find the value of x in both diagrams.

The diagram shows two intersecting lines. We can identify two pairs of angles that are vertically opposite and two pairs of angles that are supplementary (angles on a straight line).
From the visual layout and common geometry problems of this type, it is most consistent to assume:

• The angle labeled $2x+18$ and the angle labeled $72^\circ$ are supplementary angles, meaning they lie on a straight line and their sum is $180^\circ$.
• The angle labeled $x$ and the angle labeled $y$ are vertically opposite angles, meaning they are equal.

Since $2x+18$ and $72^\circ$ are supplementary:

$$(2x+18) + 72 = 180^\circ$$

Combine the constant terms:

$$2x + (18 + 72) = 180^\circ$$ $$2x + 90 = 180^\circ$$

Subtract $90^\circ$ from both sides:

$$2x = 180^\circ - 90^\circ$$ $$2x = 90^\circ$$

Divide by 2:

$$x = \frac{90^\circ}{2}$$ $$x = 45^\circ$$

The angle $x$ and the angle $y$ are vertically opposite, so they are equal:

$$y = x$$

Substitute the value of $x$ found in Step 3 into the equation from Step 4:

$$y = 45^\circ$$

The values of the unknown angles are:
$x = \boxed{45^\circ}$
$y = \boxed{45^\circ}$