SOLUTION: In triangle JKL, JK is congruent to KL and angle J=2x-y,angle K=2x+2y, angle L=x+2y find x and y

Algebra ->  Geometry-proofs -> SOLUTION: In triangle JKL, JK is congruent to KL and angle J=2x-y,angle K=2x+2y, angle L=x+2y find x and y      Log On


   

Question 922923: In triangle JKL, JK is congruent to KL and angle J=2x-y,angle K=2x+2y, angle L=x+2y
find x and y
Answer by MathLover1(20850) About Me  (Show Source):
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In triangle JKL, JK is congruent to KL=> then we have an isosceles triangle which means angles J and L are congruent

given:
angle J=2x-y
angle L=x%2B2y+
angle K=2x%2B2y
J=L
2x-y=x%2B2y
2x-x=y%2B2y
x=3y
=> J=2%2A3y-y=> J=6y-y=> J=5y
=>L=x%2B2y+=>L=3y%2B2y+=>L=5y+and
=>K=2x%2B2y=>K=2%2A3y%2B2y=>K=6y%2B2y=>K=8y
now, we also know that the sum of all angles in triangle is 180
J%2BL%2BK=180
5y%2B5y%2B8y=180 ....solve for y
18y=180
y=180%2F18
highlight%28y=10%29
now find x
x=3y
x=3%2A10
highlight%28x=30%29

since you know x and y, you can find the measure of the angles too:
J=5y=>J=50
L=5y=>L=50
K=8y=>K=80