Ray LC is an angle bisector of JLY, JLC = (6x+1), and JLY = (10x+16).

What is JLC?

Bisector divides the angle into 2 equal parts

since it a bisector

JLC=1/2 of JLY

solve for x then add them and solve for JLY

JLC=1/2 times JLY

JLC=6x+1

JLY=10x+16

subsitute

6x+1=1/2 (10x+16)

distribute

1/2 (10x+16) = 5x+8

6x+1=5x+8

subtrac 5x from both sides

x+1=8

subtract 1

x=7

JLC=6x+1

subsitute

x=7

JLC=6 (7) + 1

JLC=42+1

JLC=43

answer is JLC is 43 degrees

diagram included to show what bisector is