Answer:
The values of x and y are: \(90^{\circ}\) and \(43^{\circ}\)
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 \(47^{\circ}\).
By the definition, the isosceles triangle has two congruent base i.e \(\angle B =\angle C\).
⇒\(\angle B=47^{\circ}\)
Angle Bisector means A line AD splits an angle A into two equal angles i.e, \(\angle A=2 y^{\circ}\)
Now, by the triangle angle sum theorem, sum of the measure of the angle in triangle ABC is \(180^{\circ}\).
therefore, we have in triangle ABC,
\(\angle A +\angle B+\angle C =180^{\circ}\)
putting the values of angles A, angle B and angle C to find the value of y.
\(2 y^{\circ}+47^{\circ}+47^{\circ}=180^{\circ}\)
\(2 y^{\circ}+94^{\circ}=180^{\circ}\)
\(2 y^{\circ}=86^{\circ}\)
simplify we get, \(y=43^{\circ}\)
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 \(180^{\circ}\)
∴ \(y +\angle B+x=180^{\circ}\)
\(43^{\circ}+47+x=180^{\circ}\)
\(90^{\circ}+x=180^{\circ}\)
⇒ \(x=90^{\circ}\)
Therefore, the values of x and y are: \(90^{\circ}\) and \(43^{\circ}\)
