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°
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SOQ = 140°
