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,
[tex]AB=AC[/tex] (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,
[tex]\angle B\cong \angle C[/tex]
[tex]m\angle B\cong m\angle C[/tex]
[tex]m\angle B\cong 49^\circ[/tex]
The angle bisector of an isosceles triangle is the median and altitude of the triangle. So, the angle bisector is perpendicular to the base.
[tex]m\angle ADB=90^\circ[/tex]
[tex]x^\circ=90^\circ[/tex]
In triangle ABD,
[tex]m\angle DAB+m\angle ABD+m\angle ADB=180^\circ[/tex] [Angle sum property]
[tex]y^\circ+49^\circ+x^\circ=180^\circ[/tex]
[tex]y^\circ+49^\circ+90^\circ=180^\circ[/tex]
[tex]y^\circ=180^\circ-49^\circ-90^\circ[/tex]
[tex]y^\circ=41^\circ[/tex]
Therefore, the correct option is B.
