Option D. y= 36
Step-by-step explanation:
In the given figure there are two triangles ΔMPO and ΔMNL
If two sides OP and LN are parallel and lines MN, ML are transverse respectively.
Then ∠MPO =∠MNL [ corresponding angles ]
and ∠MOP = ∠MLN [ corresponding angles ]
and ∠M is common to both the triangles.
Now by the property of AAA, ΔMPO & ΔMNL are similar
Now we know in similar triangles corresponding sides are in same ratio.
![\frac{MP}{MN}=\frac{MO}{ML}](/tpl/images/0279/2088/51234.png)
![\frac{y}{y+18}=\frac{28}{28+14}=\frac{28}{42}=\frac{2}{3}](/tpl/images/0279/2088/f6c54.png)
By cross multiplication
3y = 2(y + 18)
3y = 2y + 36
y = 36
Option D. y = 36 is the answer.