To find:
The value of y.
Solution:
The line is an angle bisector. The angle bisector bisects the side opposite to the angle in the same ratio equal to ratio of other two sides.
So, in the ratio:
[tex]\frac{y+4}{2y+5}=\frac{4}{6}[/tex]
Solve the above equation for y:
[tex]\begin{gathered} \frac{y+4}{2y+5}=\frac{4}{6} \\ 6(y+4)=4(2y+5) \\ 6y+24=8y+20 \\ 2y=4 \\ y=2 \end{gathered}[/tex]
Thus, the value of y is 2.
