It seems there is two ways to solve this, remember that this is just one of them.
The triangle to the left is an isosceles triangle by definition. It is given that two of its sides are equal.
The angles opposite the equal sides in an isosceles triangle are congruent. It is given that one of these angles is 70 degrees, so the other one must be 70 degrees as well.
This angle is opposite to Angle Y. Vertical angles are congruent, so Angle Y must be 70 degrees.
