How to justify construction of 90 degrees angle

Hi,
For justifying construction of 90 degrees angle first  follow all the steps.
The below given steps will be followed to construct an angle of 90°.(i) Take the given ray PQ. Draw an arc of some radius taking point P as its centre, which intersects PQ at R.(ii) Taking R as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at S.(iii) Taking S as centre and with the same radius as before, draw an arc intersecting the arc at T (see figure).(iv) Taking S and T as centre, draw an arc of same radius to intersect each other at U.(v) Join PU, which is the required ray making 90° with the given ray PQ.

JUSTIFICATION :-
You can justify it by proving ∠UPQ = 90°. For that join PS and PT.

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