To find the value of $y$, we analyze the triangle shown in the diagram.

Step 1: Recall the triangle angle sum property.

The sum of all angles in a triangle is always $180^\circ$.

Step 2: Identify the known angles.

• Two angles are already provided: $35^\circ$ and $35^\circ$.
• Let the third angle be $y$.

Step 3: Set up the equation for the angle sum.

$35^\circ + 35^\circ + y = 180^\circ$

Step 4: Solve for $y$.

$70^\circ + y = 180^\circ$ $y = 180^\circ - 70^\circ$ $y = 110^\circ$

Final Answer:

$y = 110^\circ$

If you have any questions or would like further details, let me know! Here are some related questions:

1. What are the properties of an isosceles triangle, and how do they apply here?
2. How does the triangle inequality relate to angles in a triangle?
3. Could you find the length of the sides if more information was given?
4. How does this problem change if the angles were $30^\circ$ instead of $35^\circ$?
5. Why is it important to verify the sum of all angles in a triangle?

Tip: Always check your work by verifying that the angles sum to $180^\circ$.