Answer:
The values of x and y are: [tex]90^{\circ}[/tex] and [tex]43^{\circ}[/tex]
Step-by-step explanation:
An isosceles triangle has two congruent sides and two congruent base angles.
Given triangle ABC is an isosceles triangle , since it has two congruent sides i.e AB=AC .
also given in the triangle the base angle C is [tex]47^{\circ}[/tex].
By the definition, the isosceles triangle has two congruent base i.e [tex]\angle B =\angle C[/tex].
⇒[tex]\angle B=47^{\circ}[/tex]
Angle Bisector means A line AD splits an angle A into two equal angles i.e, [tex]\angle A=2 y^{\circ}[/tex]
Now, by the triangle angle sum theorem, sum of the measure of the angle in triangle ABC is [tex]180^{\circ}[/tex].
therefore, we have in triangle ABC,
[tex]\angle A +\angle B+\angle C =180^{\circ}[/tex]
putting the values of angles A, angle B and angle C to find the value of y.
[tex]2 y^{\circ}+47^{\circ}+47^{\circ}=180^{\circ}[/tex]
[tex]2 y^{\circ}+94^{\circ}=180^{\circ}[/tex]
[tex]2 y^{\circ}=86^{\circ}[/tex]
simplify we get, [tex]y=43^{\circ}[/tex]
Now, to find the values of x , we again use the triangle angle sum theorem, sum of the measure of the angle in triangle ADC is [tex]180^{\circ}[/tex]
∴ [tex]y +\angle B+x=180^{\circ}[/tex]
[tex]43^{\circ}+47+x=180^{\circ}[/tex]
[tex]90^{\circ}+x=180^{\circ}[/tex]
⇒ [tex]x=90^{\circ}[/tex]
Therefore, the values of x and y are: [tex]90^{\circ}[/tex] and [tex]43^{\circ}[/tex]
