Answer : The value of x and y is, [tex]90^o[/tex] and [tex]43^oC[/tex]
Step-by-step explanation :
First we have to calculate the angle B.
As we know that,
The given triangle is an isosceles triangle in which the angles opposite to equal sides are always equal.
Thus, [tex]\angle B=\angle C[/tex]
Given : [tex]\angle C=47^o[/tex]
[tex]\angle B=\angle C=47^o[/tex]
[tex]\angle B=47^o[/tex]
Now have to calculate the angle A.
As we know that the sum of interior angles of a triangle is equal to [tex]180^o[/tex].
[tex]\angle A+\angle B+\angle C=180^o[/tex]
[tex]\angle A+47^o+47^o=180^o[/tex]
[tex]\angle A+94^o=180^o[/tex]
[tex]\angle A=180^o-94^o[/tex]
[tex]\angle A=86^o[/tex]
Now we have to determine the angle y.
As we know that, line AD is an angle bisector. That means, it divides into two equal angles. So,
[tex]\angle y=\frac{\angle A}{2}[/tex]
[tex]\angle y=\frac{86^o}{2}[/tex]
[tex]\angle y=43^o[/tex]
Now we have to determine the angle x.
As we know that the sum of interior angles of a triangle is equal to [tex]180^o[/tex].
[tex]\angle y+\angle B+\angle x=180^o[/tex]
[tex]43^oc+47^o+\angle x=180^o[/tex]
[tex]\angle x+90^o=180^o[/tex]
[tex]\angle x=180^o-90^o[/tex]
[tex]\angle x=90^o[/tex]
Thus, the value of x and y is, [tex]90^o[/tex] and [tex]43^oC[/tex]
