Given equilateral xyz find the value of x and y?

If triangle XYZ is equilateral, then all three sides are equal in length. Therefore, the value of x and y would be the same.

Since the triangle is equilateral all sides are equal, so we have:

x = y

The perimeter of the triangle is the sum of the lengths of all three sides, so we have:

Perimeter = x + y + z

Since the perimeter is 30, we have:

30 = x + y + z

Substituting x = y into the equation, we get:

30 = 2x + z

We can also use the fact that the sum of the interior angles of a triangle is 180 degrees to find the value of z. Since the triangle is equilateral, all three angles are equal, so each angle is:

180 / 3 = 60 degrees

The sum of the angles in a triangle is 180 degrees, so the sum of the two angles other than z is:

180 - 60 = 120 degrees

The sum of the interior angles of a triangle is also equal to the sum of the exterior angles, so the sum of the exterior angles is:

180 - 120 = 60 degrees

The exterior angle at vertex z is equal to the sum of the two interior angles on the opposite side, so the exterior angle at vertex z is:

60 + 60 = 120 degrees

Since the sum of the exterior angles of a triangle is 360 degrees, the exterior angle at vertex z is:

360 - 120 = 240 degrees

The exterior angle at vertex z is equal to the sum of the two interior angles on the opposite side, so the sum of the two interior angles on the opposite side is:

240 - 60 = 180 degrees

Since the triangle is equilateral, all three angles are equal, so each of the two angles on the opposite side is:

180 / 2 = 90 degrees

Therefore, the value of z is:

z = 180 - 90 - 90 = 0

Since the perimeter of the triangle is 30 and the sum of the two sides is 2x, we have:

z = 30 - 2x

Since z = 0, we have:

0 = 30 - 2x

Solving for x, we get:

x = 15

Therefore, the value of x is 15 and the value of y is also 15.

X -y=12,x-z=5x-2 and 1÷3y+1