Question

Find the values of x and y.

Answer 1

X is 90°
A triangles angles add up to 180° so
180 - 47 - 90 = y
180 - 137 = y
y = 43°

Answer 2

Answer:

$x=90^{\circ}$

$y=43^{\circ}$

Step-by-step explanation:

We have been given an isosceles triangle being two sides equal AB and AC

By the property of isosceles triangle

The sides which are equal will have same base angle

Hence, ∠ABC=∠ACB=$47{^\circ}$

We know that sum of angles of triangle is $180^{\circ}$

∠ABC+ ∠ACB+∠BAC=$180^{\circ}$      (1)

Since, ∠BAC is the bisector so, ∠BAD and ∠DAC are equal which is $y^{\circ}$

Now, substituting the values in (1) we get:

$47^{\circ}+47^{\circ}+2y^{\circ}=180^{\circ}$

$94+2y^{\circ}=180^{\circ}$

$2y=86$

$y=43^{\circ}$

Now, we will consider ΔABD to find x

$∠BAD=[tex]43^{\circ}$,∠ADB=$x^{\circ}$∠ABD=$46^{\circ}$

Now, Apply the sum of angles of triangle is $180^{\circ}$ we get:

$47^{\circ}+x^{\circ}+43^{\circ}=180^{\circ}$

$90^{\circ}+x^{\circ}=180^{\circ}$

$x^{\circ}=90^{\circ}$