Note: enter your answer and show all the steps that you use to solve this problem in the space provided. triangle a b c is shown with an angle bisector and two congruent sides. side a b is congruent to side a c. segment a d is the bisector of angle a. point d is on side b c. angle b a d is labeled y degrees. angle b d a is labeled x degrees. angle a c d is labeled 47 degrees. find the values of x and y.

x=90 degrees, y=43 degrees

Step-by-step explanation:

The triangle ABC is an isosceles triangle with congruent sides AB and AC.  Therefore, the angles ABC and ACB are equal. Segment AD is the bisector of angle A (or BAC). The angle ACD is given as 47 degrees. So, angles ABC and ACB are 47 degrees each, since the point D is on side BC. The angle BAC is 180-2(47) degrees which is 86 degrees. Since AD is bisector of the angle BAC, BAD is 86/2=43 degrees . From the triangle BAD, angle of BDA is 180 - (the angle ABD + the angle BAD) = 180 -(47+43)=90 degrees. So x=90 and y=43 degrees.