Question

find the value of y.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle opposite to the $18^{\circ}$ angle is also $18^{\circ}$.

Step2: Consider the sum of angles around a point

The sum of angles around a point is $360^{\circ}$. We can set up an equation using the known angles. Let's assume the angles are arranged such that we can write the equation based on the fact that the sum of all the angles shown is $360^{\circ}$. However, we can also use the property of linear - pairs and vertical - angles. A linear - pair of angles sums to $180^{\circ}$.
We know that the angle adjacent to the $64^{\circ}$ angle and $y^{\circ}$ and the $18^{\circ}$ angle are related. First, note that the angle adjacent to the $64^{\circ}$ angle (let's call it $a$) and $64^{\circ}$ form a linear - pair, so $a = 180 - 64=116^{\circ}$.
Since $y$ and the angle composed of the $18^{\circ}$ angle and the adjacent part of the $64^{\circ}$ angle are vertical - angles.
We know that $y=18 + 64$.

Step3: Calculate the value of y

$y=18 + 64=82$.

Answer:

$82$