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.

Question

asked Dec 11, 2021 34.1k views

1 Answer

Yannick · Answer 1 · 2021-12-16T04:34:14+0000

Answer:

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.