Y= 49 degrees
Isosceles triangles which are triangles that have two side of equal length will also have two angles that are equal. Since you know BC=CD that means their corresponding angles are equal. To set this up you can do:
180=2Y+82
Solve for Y. 180 because a triangles angles add up to 180. Then subtract 82 on both sides. Which gives you 98. Then you divide 98 by 2. And that will give you 49.