find the values of x and y.\n\nx = (simplify your answer.)

Explanation:

Step1: Use the property of isosceles triangles

Since (AB = BC) and (AD = DC), (\triangle ABD\cong\triangle CBD) (by SSS - Side - Side - Side congruence criterion). So, (\angle ABD=\angle CBD). In (\triangle ABD), using the angle - sum property of a triangle ((\angle A+\angle ABD+\angle ADB = 180^{\circ})), but we can also note that for (\angle ABD), given (\angle A = 51^{\circ}) and (\triangle ABD) is part of the congruent triangles. We know that in (\triangle ABD), (\angle ABD) can be found as follows: Since (\triangle ABD) and (\triangle CBD) are congruent and (AB = BC), (AD = DC), (BD=BD). The angle (\angle ABD) is calculated as (x = 51^{\circ}) (because (\triangle ABD\cong\triangle CBD) and corresponding angles of congruent triangles are equal).

Answer:

(x = 51)