Question

Find the values of x and y

Answer 1

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 $43^{\circ}$

Answer 2

Pretty sure x is 90 and y is 43.