Find the value of x in both diagrams.

This problem involves finding unknown angles formed by intersecting lines. The image is a bit blurry, but we can identify the angles and their relationships.

Step 1: Identify the relationships between the angles. 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.

Step 2: Formulate the first equation using supplementary angles. Since $2x+18$ and $72^\circ$ are supplementary: $(2x+18) + 72 = 180^\circ$

Step 3: Solve for $x$. 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: $x = \frac{90^\circ}{2}$ $x = 45^\circ$

Step 4: Formulate the second equation using vertically opposite angles. The angle $x$ and the angle $y$ are vertically opposite, so they are equal: $y = x$

Step 5: Solve for $y$. 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: $x = \boxed{45^\circ}$ $y = \boxed{45^\circ}$