Find the values of x and y.
a. x=55, y=35
b. x=90, y=55
c. x=90, y=35
d. x=35, y=55

x = 90
y = 35

Explanation:
1- getting the value of x:
We are given that AC = AB. This means that ΔABC is an isosceles triangle.
We are also given that AD bisects angle A.
Now, in an isosceles triangle, the angle bisector is perpendicular to the base.
We have:
isosceles triangle ABC, BC as a base and AD as an angle bisector
Therefore:
AD is perpendicular on BC
This means that:
measure angle ADB = x = 90°

2- getting the value of y:
Since triangle ABC is an isosceles triangle, therefore:
measure angle C = measure angle B = 55°
We know that sum of interior angles in a triangle is 180.
In triangle ADB, we have:
measure angle B = 55°
measure angle ADB = 90°
measure angle BAD = y
Therefore:
55 + 90 + y = 180
y = 180 - 55 - 90
y = 35°

Hope this helps :)