Given:
In triangle ABC, AB = AC, AD is angle bisector and measure of angle C is 49 degrees.
To find:
The value of x and y.
Solution:
In triangle ABC,
(Given)
So, triangle ABC is an isosceles triangle and by the definition of base angles the base angles of isosceles triangle are congruent.
In isosceles triangle ABC,
The angle bisector of an isosceles triangle is the median and altitude of the triangle. So, the angle bisector is perpendicular to the base.
In triangle ABD,
[Angle sum property]
Therefore, the correct option is B.