Find the values of X and Y.

Given:

A figure.

To find:

The value of x and y.

Solution:

In triangle ADC, all angles are equal, so it is an equilateral triangle.

We know that, all sides of an equilateral triangle are equal.

      ...(i)

                  ...(ii)

In triangle ABD,

Base angles are equal, so triangle ABD is an isosceles triangle.

    ...(iii)

Using (i) and (iii), we get

Divide both sides by 4.

Putting y=4 in (ii), we get

Adding 5 on both sides, we get

Divide both sides by 3.

[tex]x=7/tex]

Therefore, the value of x is 7 and the value of y is 4.