Given as shown in the figure :
The triangle ABC is isosceles triangle
The measure of the angle A = 54
So, the measure of the angle C = The measure of the angle A = 54
The sum of the angles of the triangle = 180
So, the measure of the angle ABC = 180 - ( 54 + 54 ) = 180 - 108 = 72
And as shown BD bisects the angle ABC
So, x = half of the angle ABC
X = 0.5 * 72 = 36
The triangles ABD and CBD have the following :
1. AB = BC : Given
2. m∠ABD = m∠CBD : proved
3. BD = BD : reflexive property
So, the triangle ABD congruent to the the triangle CBD
So, CPCTC
so,
AD = CD
AD = 5
So,
y = CD = 5
So, the answer is :
x = 36
y = 5