In the given figure , if angel roq = 90 and angel pos : angel ros = 4 : 5 , then the value of angel soq is

First of all, these are angles.  'Angels' don't pop up too often in math.

ROQ is 90°.

Then POR is also 90°.

POS : ROS = 4 : 5

So if you split up POR into (4 + 5) = 9 pieces, POS is 4 of them and ROS is 5 of them.  

Since POR is 90°, each piece is 10° .

POS = 40°
and
ROS = 50° .

SOQ is ROS added onto ROQ.

ROQ = 90°
ROS = 50°

SOQ = 140°