Find the values of x and y. in triangle jkl, jk = kl, angle j = 2x-y, angle k = 2x+2y, and angle l = x+2y.

Step-by-step explanation:

The relationship of sides tells you that angle L is congruent to angle J, so ...

  x +2y = 2x -y

  3y = x . . . . . . . . add y-x to both sides

The sum of angles in a triangle is always 180 degrees, so ...

  (2x -y) +(2x +2y) +(x +2y) = 180

  5x +3y = 180 . . . . simplify

  5x +x = 180 . . . . . substitute for 3y using the above relation

  x = 180/6 = 30

  y = x/3 = 10

The values of x and y are 30 and 10, respectively.

Check

  J = 2(30) -10) = 50

  K = 2(30+10) = 80

  L = 30 +2(10) = 50

Angles J and L have the same measure, and the sum of all is 180.